System and method for reducing nyquist ghost artifact

ABSTRACT

A method and system for reducing Nyquist ghost artifact is provide. The method may include: obtaining a plurality of measured data sets; determining, based on the plurality of measured data sets, in a data space, a plurality of convolution kernels, each convolution kernel relating to all of the plurality of measured data sets; generating, based on the plurality of convolution kernels and the plurality of measured data sets, in the data space, a plurality of synthetic data sets; generating, based on the plurality of synthetic data sets and the plurality of measured data sets, in the data space, a plurality of combined data sets, each combined data set relating to one of the plurality of synthetic data sets and a corresponding measured data set of the plurality of measured data sets; and reconstructing, based on the plurality of combined data sets, an image.

TECHNICAL FIELD

The present disclosure generally relates to image processing, and morespecifically relates to a system and method for reducing Nyquist ghostartifact in an image produced by echo planar imaging (EPI).

BACKGROUND

Magnetic resonance imaging (MRI) is widely used. An MRI image may beproduced by exploiting a powerful magnetic field and radiofrequency (RF)techniques. During an MRI process, a plurality of acquired RF signalsmay be filled into k-space. The data in k-space may be transformed toreconstruct an MRI image. Echo planar imaging (EPI) is a fast imagingtechnique. A whole image may be produced within 30 milliseconds usingEPI. The EPI technique may use a reverse direction frequency readoutgradient to obtain one or more odd echoes and even echoes in turns. Theodd echoes and even echoes in k-space may correspond to a plurality ofMR signals acquired with opposite readout gradient polarities,respectively. Due to the eddy current induced by high-speed switching ofthe gradient magnetic field, phase inconsistencies (or phase errors) maybe induced between the odd echoes and even echoes (or between theplurality of MR signals acquired with opposite readout gradientpolarities). The existence of phase inconsistencies in k-space data mayin turn generate Nyquist ghost artifact in a reconstructed image.

Nyquist ghost artifact may be common in images produced by EPI. One ormore traditional techniques may only correct phase errors along areadout (i.e., frequency encoding) direction (also referred to asone-dimensional (1D) phase correction). However, residual artifacts maystill exist after such a 1D phase correction. Thus, it is desirable toprovide a two-dimensional (2D) phase correction technique to reduce orremove Nyquist ghost artifact.

SUMMARY

In one aspect of the present disclosure, a method implemented on acomputing device is provided. The computing device may have at least oneprocessor, at least one computer-readable storage medium, and acommunication port connected to an imaging device, the imaging deviceincluding a plurality of radiofrequency (RF) coils for receiving aplurality of channels of magnetic resonance (MR) signals. The method mayinclude: a) obtaining a plurality of measured data sets; b) determining,based on the plurality of measured data sets, in a data space, aplurality of convolution kernels, each convolution kernel relating toall of the plurality of measured data sets, each convolution kernelcorresponding to a channel of MR signal received by an RF coil; c)generating, based on the plurality of convolution kernels and theplurality of measured data sets, in the data space, a plurality ofsynthetic data sets, wherein each synthetic data set is generated basedon one or more of the plurality of measured data sets and acorresponding convolution kernel of the plurality of convolutionkernels, and wherein each synthetic data set and the correspondingconvolution kernel correspond to a same channel; d) generating, based onthe plurality of synthetic data sets and the plurality of measured datasets, in the data space, a plurality of combined data sets, eachcombined data set relating to one of the plurality of synthetic datasets and a corresponding measured data set of the plurality of measureddata sets; and e) reconstructing, based on the plurality of combineddata sets, an image.

In some embodiments, the plurality of measured data sets may begenerated by echo planar imaging (EPI) using the imaging device. Eachmeasured data set may correspond to a channel of MR signal received byan RF coil.

In some embodiments, the plurality of measured data sets may beprocessed by performing a preliminary correction for the plurality ofmeasured data sets.

In some embodiments, the method may further include performing aplurality of iterations. In each current iteration, the method mayinclude designating the plurality of combined data sets generated in aprevious iteration as the plurality of measured data sets; repeatingb)-d) to update the plurality of combined data sets; and determiningwhether the plurality of updated combined data sets generated in thecurrent iteration satisfy a termination criterion.

In some embodiments, the termination criterion may relate to adifference between the plurality of combined data sets generated in theprevious iteration and the plurality of updated combined data setsgenerated in the current iteration.

In some embodiments, the generating a plurality of combined data setsmay include determining, based on a plurality of weighting factors, aweighted sum of the plurality of synthetic data sets and the pluralityof measured data sets to obtain the plurality of combined data sets.Each combined data set may be determined based on a portion of theplurality of weighting factors, one of the plurality of synthetic datasets, and a corresponding measured data set of the plurality of measureddata sets.

In some embodiments, each measured data set of the plurality of measureddata sets may include a full k-space data set.

In some embodiments, the reconstructing an image may include processingthe plurality of combined data sets with an inverse Fourier transform togenerate the image.

In some embodiments, at least one measured data set of the plurality ofmeasured data sets may include a partially filled k-space data set.

In some embodiments, the reconstructing an image may include for eachmeasured data set including a partially filled k-space data set,filling, based on at least a portion of the plurality of combined datasets, a corresponding combined data set to reconstruct a full k-spacedata set; and processing a plurality of full k-space data setscorresponding to the plurality of combined data sets with an inverseFourier transform to generate the image.

In some embodiments, the data space may be a k-space.

In some embodiments, the data space may be an intermediate space betweenk-space and an image space. The method may further include determiningthe intermediate space by processing k-space with a one-dimensional (1D)inverse Fourier transform.

In some embodiments, at least two convolution kernels of the pluralityof convolution kernels may be different.

In some embodiments, at least two convolution kernels for a same channelgenerated in different iterations may be different.

In another aspect of the present disclosure, a magnetic resonanceimaging (MRI) method is provided. The method may include generating aplurality of magnetic resonance (MR) signals by scanning a subject usingan imaging device. The method may also include receiving the pluralityof MR signals using a plurality of radiofrequency (RF) coils of theimaging device. The method may further include obtaining a plurality ofmeasured k-space data sets by entering the MR signals into k-space. Eachmeasured k-space data set may correspond to one of the plurality of RFcoils. The method may further include performing one or more correctionsfor the plurality of measured k-space data sets to obtain a plurality ofcorrected k-space data sets; and reconstructing, based on the pluralityof corrected k-space data sets, an image related to the subject. The oneor more corrections may include determining, based on the plurality ofmeasured k-space data sets, a plurality of convolution kernels;generating, based on the plurality of convolution kernels and theplurality of measured k-space data sets, a plurality of synthetick-space data sets; and generating, based on the plurality of synthetick-space data sets and the plurality of measured k-space data sets, theplurality of corrected k-space data sets.

In some embodiments, the method may further include before determiningthe plurality of convolution kernels, performing a linear or non-linearcorrection for the plurality of measured k-space data sets.

In some embodiments, the determining a plurality of convolution kernelsmay include processing the plurality of measured k-space data sets withone-dimensional (1D) inverse Fourier transform to obtain an intermediateimage; and determining, based on the intermediate image, the pluralityof convolution kernels.

In yet another aspect of the preset disclosure, a system is provided.The system may include at least one storage medium storing a set ofinstructions; at least one processor in communication with the at leastone storage medium; and a communication port connected to an imagingdevice, the imaging device including a plurality of radiofrequency (RF)coils for receiving a plurality of channels of magnetic resonance (MR)signals. When executing the set of instructions, the at least oneprocessor may be configured to cause the system to: a) obtain aplurality of measured data sets; b) determine, based on the plurality ofmeasured data sets, in a data space, a plurality of convolution kernels,each convolution kernel relating to all of the plurality of measureddata sets, each convolution kernel corresponding to a channel of MRsignal received by an RF coil; c) generate, based on the plurality ofconvolution kernels and the plurality of measured data sets, in the dataspace, a plurality of synthetic data sets, wherein each synthetic dataset is generated based on one or more of the plurality of measured datasets and a convolution kernel of the plurality of convolution kernels,and wherein each synthetic data set and the convolution kernelcorrespond to a same channel; d) generate, based on the plurality ofsynthetic data sets and the plurality of measured data sets, in the dataspace, a plurality of combined data sets, each combined data setrelating to one of the plurality of synthetic data sets and acorresponding measured data set of the plurality of measured data sets;and e) reconstruct, based on the plurality of combined data sets, animage.

In some embodiments, each measured data set of the plurality of measureddata sets may include a full k-space data set.

In some embodiments, at least one measured data set of the plurality ofmeasured data sets may include a partially filled k-space data set.

In some embodiments, the data space may be k-space or an intermediatespace between k-space and an image space.

In yet another aspect of the present disclosure, a non-transitorycomputer readable medium is provided. The non-transitory computerreadable medium may include executable instructions that, when executedby at least one processor, may cause the at least one processor toeffectuate a method including: a) obtaining a plurality of measured datasets; b) determining, based on the plurality of measured data sets, in adata space, a plurality of convolution kernels, each convolution kernelrelating to all of the plurality of measured data sets, each convolutionkernel corresponding to a channel of MR signal received by an RF coil;c) generating, based on the plurality of convolution kernels and theplurality of measured data sets, in the data space, a plurality ofsynthetic data sets, wherein each synthetic data set is generated basedon one or more of the plurality of measured data sets and a convolutionkernel of the plurality of convolution kernels, and wherein eachsynthetic data set and the convolution kernel correspond to a samechannel; d) generating, based on the plurality of synthetic data setsand the plurality of measured data sets, in the data space, a pluralityof combined data sets, each combined data set relating to one of theplurality of synthetic data sets and a corresponding measured data setof the plurality of measured data sets; and e) reconstructing, based onthe plurality of combined data sets, an image.

In some embodiments, a system is provided. The system may include atleast one storage medium storing a set of instructions; and at least oneprocessor in communication with the at least one storage medium. Whenexecuting the set of instructions, the at least one processor may beconfigured to cause the system to generate a plurality of magneticresonance (MR) signals by scanning a subject using an imaging device.The at least one processor may be further configured to cause the systemto receive the plurality of MR signals using a plurality ofradiofrequency (RF) coils of the imaging device. The at least oneprocessor may be also configured to cause the system to obtain aplurality of measured k-space data sets by entering the MR signals intok-space, each measured k-space data set corresponding to one of theplurality of RF coils. The at least one processor may be furtherconfigured to cause the system to perform one or more corrections forthe plurality of measured k-space data sets to obtain a plurality ofcorrected k-space data sets; and reconstruct, based on the plurality ofcorrected k-space data sets, an image related to the subject. The one ormore corrections may include determining, based on the plurality ofmeasured k-space data sets, a plurality of convolution kernels;generating, based on the plurality of convolution kernels and theplurality of measured k-space data sets, a plurality of synthetick-space data sets; and generating, based on the plurality of synthetick-space data sets and the plurality of measured k-space data sets, theplurality of corrected k-space data sets.

In some embodiments, the at least one processor may be furtherconfigured to cause the system to before determining the plurality ofconvolution kernels, perform a linear or non-linear correction for theplurality of measured k-space data sets.

In some embodiments, the determining a plurality of convolution kernelsmay include processing the plurality of measured k-space data sets withone-dimensional (1D) inverse Fourier transform to obtain an intermediateimage; and determining, based on the intermediate image, the pluralityof convolution kernels.

In yet another aspect of the present disclosure, a non-transitorycomputer readable medium is provided. The non-transitory computerreadable medium may include executable instructions that, when executedby at least one processor, may cause the at least one processor toeffectuate a method including generating a plurality of magneticresonance (MR) signals by scanning a subject using an imaging device;receiving the plurality of MR signals using a plurality ofradiofrequency (RF) coils of the imaging device; obtaining a pluralityof measured k-space data sets by entering the MR signals into k-space,each measured k-space data set corresponding to one of the plurality ofRF coils; performing one or more corrections for the plurality ofmeasured k-space data sets to obtain a plurality of corrected k-spacedata sets; and reconstructing, based on the plurality of correctedk-space data sets, an image related to the subject. The one or morecorrections may include determining, based on the plurality of measuredk-space data sets, a plurality of convolution kernels; generating, basedon the plurality of convolution kernels and the plurality of measuredk-space data sets, a plurality of synthetic k-space data sets; andgenerating, based on the plurality of synthetic k-space data sets andthe plurality of measured k-space data sets, the plurality of correctedk-space data sets.

In yet another aspect of the present disclosure, a system having atleast one processor and a storage configured to store instructions isprovided. The system may include a data acquisition module configured toobtain a plurality of measured data sets using an imaging device, theimaging device including a plurality of radiofrequency (RF) coils forreceiving a plurality of channels of magnetic resonance (MR) signals.Each measured data set may correspond to a channel of MR signal receivedby an RF coil. The system may further include a convolution kerneldetermination unit configured to determine, based on the plurality ofmeasured data sets, in a data space, a plurality of convolution kernels.Each convolution kernel may relate to all of the plurality of measureddata sets. Each convolution kernel may correspond to a channel of MRsignal received by an RF coil. The system may also include a syntheticdata generation unit configured to generate, based on the plurality ofconvolution kernels and the plurality of measured data sets, in the dataspace, a plurality of synthetic data sets. Each synthetic data set maybe generated based on one or more of the plurality of measured data setsand a convolution kernel of the plurality of convolution kernels. Eachsynthetic data set and the convolution kernel may correspond to a samechannel. The system may further include a combined data generation unitconfigured to generate, based on the plurality of synthetic data setsand the plurality of measured data sets, in the data space, a pluralityof combined data sets. Each combined data set may relate to one of theplurality of synthetic data sets and a corresponding measured data setof the plurality of measured data sets. The system may further includean image reconstruction module configured to reconstruct, based on theplurality of combined data sets, an image.

In some embodiments, each measured data set of the plurality of measureddata sets may include a full k-space data set.

In some embodiments, at least one measured data set of the plurality ofmeasured data sets may include a partially filled k-space data set.

In some embodiments, the data space may be k-space or an intermediatespace between k-space and an image space.

Additional features will be set forth in part in the description whichfollows, and in part will become apparent to those skilled in the artupon examination of the following and the accompanying drawings or maybe learned by production or operation of the examples. The features ofthe present disclosure may be realized and attained by practice or useof various aspects of the methodologies, instrumentalities andcombinations set forth in the detailed examples discussed below.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is further described in terms of exemplaryembodiments. These exemplary embodiments are described in detail withreference to the drawings. The drawings are not to scale. Theseembodiments are non-limiting exemplary embodiments, in which likereference numerals represent similar structures throughout the severalviews of the drawings, and wherein:

FIG. 1 is a schematic diagram illustrating an exemplary magneticresonance imaging (MRI) system according to some embodiments of thepresent disclosure;

FIG. 2 is a schematic diagram illustrating exemplary hardware and/orsoftware components of an exemplary computing device on which theprocessing device may be implemented according to some embodiments ofthe present disclosure;

FIG. 3 is a schematic diagram illustrating exemplary hardware and/orsoftware components of an exemplary mobile device according to someembodiments of the present disclosure;

FIG. 4 is a block diagram illustrating an exemplary processing deviceaccording to some embodiments of the present disclosure;

FIG. 5 is a block diagram illustrating an exemplary data correctionmodule according to some embodiments of the present disclosure;

FIG. 6 is a flowchart illustrating an exemplary process for generatingan image with reduced or no Nyquist ghost artifact according to someembodiments of the present disclosure;

FIGS. 7A and 7B are schematic diagrams illustrating exemplary echoesfilled into k-space according to some embodiments of the presentdisclosure;

FIG. 8 is a flowchart illustrating an exemplary process for performing apreliminary correction for measured data set(s) according to someembodiments of the present disclosure;

FIG. 9 is a flowchart illustrating an exemplary process for generatingone or more combined data sets according to some embodiments of thepresent disclosure;

FIGS. 10A-10D are schematic diagrams illustrating exemplary measureddata sets, an exemplary convolution kernel, exemplary synthetic datasets, and exemplary combined data sets according to some embodiments ofthe present disclosure;

FIGS. 11A and 11B are exemplary images processed by 1D correction withdifferent brightness; and

FIGS. 11C and 11D are exemplary images processed by 2D correction withdifferent brightness.

DETAILED DESCRIPTION

In the following detailed description, numerous specific details are setforth by way of examples in order to provide a thorough understanding ofthe relevant disclosure. However, it should be apparent to those skilledin the art that the present disclosure may be practiced without suchdetails. In other instances, well known methods, procedures, systems,components, and/or circuitry have been described at a relativelyhigh-level, without detail, in order to avoid unnecessarily obscuringaspects of the present disclosure. Various modifications to thedisclosed embodiments will be readily apparent to those skilled in theart, and the general principles defined herein may be applied to otherembodiments and applications without departing from the spirit and scopeof the present disclosure. Thus, the present disclosure is not limitedto the embodiments shown, but to be accorded the widest scope consistentwith the claims.

The terminology used herein is for the purpose of describing particularexample embodiments only and is not intended to be limiting. As usedherein, the singular forms “a,” “an,” and “the” may be intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprise,”“comprises,” and/or “comprising,” “include,” “includes,” and/or“including,” when used in this specification, specify the presence ofstated features, integers, steps, operations, elements, and/orcomponents, but do not preclude the presence or addition of one or moreother features, integers, steps, operations, elements, components,and/or groups thereof.

It will be understood that the term “system,” “unit,” “module,” and/or“block” used herein are one method to distinguish different components,elements, parts, section or assembly of different level in ascendingorder. However, the terms may be displaced by another expression if theyachieve the same purpose.

Generally, the word “module,” “unit,” or “block,” as used herein, refersto logic embodied in hardware or firmware, or to a collection ofsoftware instructions. A module, a unit, or a block described herein maybe implemented as software and/or hardware and may be stored in any typeof non-transitory computer-readable medium or other storage device. Insome embodiments, a software module/unit/block may be compiled andlinked into an executable program. It will be appreciated that softwaremodules can be callable from other modules/units/blocks or fromthemselves, and/or may be invoked in response to detected events orinterrupts. Software modules/units/blocks configured for execution oncomputing devices (e.g., processor 210 as illustrated in FIG. 2) may beprovided on a computer readable medium, such as a compact disc, adigital video disc, a flash drive, a magnetic disc, or any othertangible medium, or as a digital download (and can be originally storedin a compressed or installable format that needs installation,decompression, or decryption prior to execution). Such software code maybe stored, partially or fully, on a storage device of the executingcomputing device, for execution by the computing device. Softwareinstructions may be embedded in firmware, such as an EPROM. It will befurther appreciated that hardware modules/units/blocks may be includedof connected logic components, such as gates and flip-flops, and/or canbe included of programmable units, such as programmable gate arrays orprocessors. The modules/units/blocks or computing device functionalitydescribed herein may be implemented as software modules/units/blocks,but may be represented in hardware or firmware. In general, themodules/units/blocks described herein refer to logicalmodules/units/blocks that may be combined with othermodules/units/blocks or divided into sub-modules/sub-units/sub-blocksdespite their physical organization or storage.

It will be understood that when a unit, engine, module or block isreferred to as being “on,” “connected to,” or “coupled to,” anotherunit, engine, module, or block, it may be directly on, connected orcoupled to, or communicate with the other unit, engine, module, orblock, or an intervening unit, engine, module, or block may be present,unless the context clearly indicates otherwise. As used herein, the term“and/or” includes any and all combinations of one or more of theassociated listed items.

These and other features, and characteristics of the present disclosure,as well as the methods of operation and functions of the relatedelements of structure and the combination of parts and economies ofmanufacture, may become more apparent upon consideration of thefollowing description with reference to the accompanying drawings, allof which form a part of this disclosure. It is to be expresslyunderstood, however, that the drawings are for the purpose ofillustration and description only and are not intended to limit thescope of the present disclosure. It is understood that the drawings arenot to scale.

The following description is provided with reference to an imageprocessing technique for reducing or removing Nyquist ghost artifact.This is not intended to limit the scope the present disclosure. Forpersons having ordinary skills in the art, a certain amount ofvariations, changes, and/or modifications may be deducted under theguidance of the present disclosure. Those variations, changes, and/ormodifications do not depart from the scope of the present disclosure.

FIG. 1 is a schematic diagram illustrating an exemplary magneticresonance imaging (MRI) system 100 according to some embodiments of thepresent disclosure. As illustrated, the MRI system 100 may include anMRI scanner 110, a network 120, one or more terminals 130, a processingdevice 140, and a storage device 150. The components in the MRI system100 may be connected in one or more of various ways. Merely by way ofexample, as illustrated in FIG. 1, the MRI scanner 110 may be connectedto the processing device 140 through the network 120. As anotherexample, the MRI scanner 110 may be connected to the processing device140 directly as indicated by the bi-directional arrow in dotted lineslinking the MRI scanner and the processing device 140. As a furtherexample, the storage device 150 may be connected to the processingdevice 140 directly or through the network 120. As still a furtherexample, one or more terminals 130 may be connected to the processingdevice 140 directly (as indicated by the bi-directional arrow in dottedlines linking the terminal 130 and the processing device 140) or throughthe network 120.

The MRI scanner 110 may scan a subject located within its detectionregion and generate a plurality of data relating to the subject. In thepresent disclosure, “subject” and “object” are used interchangeably. TheMRI scanner 110 may include a magnet assembly, a gradient coil assembly,and a radiofrequency (RF) coil assembly (not shown in FIG. 1). In someembodiments, the MRI scanner 110 may be a close-bore scanner or anopen-bore scanner.

The magnet assembly may generate a first magnetic field (also referredto as a main magnetic field) for polarizing the subject to be scanned.The magnet assembly may include a permanent magnet, a superconductingelectromagnet, a resistive electromagnet, etc. In some embodiments, themagnet assembly may further include shim coils for controlling thehomogeneity of the main magnetic field.

The gradient coil assembly may generate a second magnetic field (alsoreferred to as a gradient magnetic field). The gradient coil assemblymay be designed for either a close-bore MRI scanner or an open-bore MRIscanner. The gradient coil assembly may include X-gradient coils,Y-gradient coils, and Z-gradient coils. The gradient coil assembly maygenerate one or more magnetic field gradient pulses to the main magneticfield in the X direction (Gx), Y direction (Gy), and Z direction (Gz) toencode the spatial information of the subject. In some embodiments, theX direction may be designated as a frequency encoding direction, whilethe Y direction may be designated as a phase encoding direction. In someembodiments, Gx may be used for frequency encoding or signal readout,generally referred to as frequency encoding gradient or readoutgradient. In some embodiments, Gy may be used for phase encoding,generally referred to as phase encoding gradient. In some embodiments,Gz may be used for slice selection for obtaining 2D k-space data. Insome embodiments, Gz may be used for phase encoding for obtaining 3Dk-space data.

The RF coil assembly may include a plurality of RF coils. The RF coilsmay include one or more RF transmit coils and/or one or more RF receivercoils. The RF transmit coil(s) may transmit RF pulses to the subject.Under the coordinated action of the main magnetic field, the gradientmagnetic field, and the RF pulses, MR signals relating to the subjectmay be generated. The RF receiver coils may receive MR signals from thesubject. In some embodiments, one or more RF coils may both transmit RFpulses and receive MR signals at different times. In some embodiments,the function, size, type, geometry, position, amount, and/or magnitudeof the RF coil(s) may be determined or changed according to one or morespecific conditions. For example, according to the difference infunction and size, the RF coil(s) may be classified as volume coils andlocal coils. In some embodiments, an RF receiver coil may correspond toa channel. The RF receiver coil(s) may receive a plurality of channelsof MR signals from the subject. The received MR signal(s) may be sent tothe processing device 140 directly or via the network 120 for imagereconstruction and/or image processing.

The network 120 may include any suitable network that can facilitate theexchange of information and/or data for the MRI system 100. In someembodiments, one or more components of the MRI system 100 (e.g., the MRIscanner 110, the terminal(s) 130, the processing device 140, or thestorage device 150) may communicate information and/or data with one ormore other components of the MRI system 100 via the network 120. Forexample, the processing device 140 may obtain MR signals from the MRIscanner 110 via the network 120. As another example, the processingdevice 140 may obtain user instructions from the terminal(s) 130 via thenetwork 120. In some embodiments, the network 120 may be any type ofwired or wireless network, or a combination thereof. The network 120 maybe and/or include a public network (e.g., the Internet), a privatenetwork (e.g., a local area network (LAN), a wide area network (WAN)),etc.), a wired network (e.g., an Ethernet network), a wireless network(e.g., an 802.11 network, a Wi-Fi network, etc.), a cellular network(e.g., a Long Term Evolution (LTE) network), a frame relay network, avirtual private network (“VPN”), a satellite network, a telephonenetwork, routers, hubs, switches, server computers, and/or anycombination thereof. Merely by way of example, the network 120 mayinclude a cable network, a wireline network, a fiber-optic network, atelecommunications network, an intranet, a wireless local area network(WLAN), a metropolitan area network (MAN), a public telephone switchednetwork (PSTN), a Bluetooth™ network, a ZigBee™ network, a near fieldcommunication (NFC) network, or the like, or any combination thereof. Insome embodiments, the network 120 may include one or more network accesspoints. For example, the network 120 may include wired and/or wirelessnetwork access points such as base stations and/or internet exchangepoints through which one or more components of the MRI system 100 may beconnected to the network 120 to exchange data and/or information.

The terminal 130 include a mobile device 130-1, a tablet computer 130-2,a laptop computer 130-3, or the like, or any combination thereof. Insome embodiments, the mobile device 130-1 may include a smart homedevice, a wearable device, a smart mobile device, a virtual realitydevice, an augmented reality device, or the like, or any combinationthereof. In some embodiments, the smart home device may include a smartlighting device, a control device of an intelligent electricalapparatus, a smart monitoring device, a smart television, a smart videocamera, an interphone, or the like, or any combination thereof. In someembodiments, the wearable device may include a smart bracelet, smartfootgear, a pair of smart glasses, a smart helmet, a smart watch, smartclothing, a smart backpack, a smart accessory, or the like, or anycombination thereof. In some embodiments, the smart mobile device mayinclude a smartphone, a personal digital assistance (PDA), a gamingdevice, a navigation device, a point of sale (POS) device, or the like,or any combination thereof. In some embodiments, the virtual realitydevice and/or the augmented reality device may include a virtual realityhelmet, a virtual reality glass, a virtual reality patch, an augmentedreality helmet, an augmented reality glass, an augmented reality patch,or the like, or any combination thereof. For example, the virtualreality device and/or the augmented reality device may include a GoogleGlass, an Oculus Rift, a Hololens, a Gear VR, etc. In some embodiments,the terminal(s) 130 may remotely operate the MRI scanner 110. In someembodiments, the terminal(s) 130 may operate the MRI scanner 110 via awireless connection. In some embodiments, the terminal(s) 130 mayreceive information and/or instructions inputted by a user, and send thereceived information and/or instructions to the MRI scanner 110 or tothe processing device 140 via the network 120. In some embodiments, theterminal(s) 130 may receive data and/or information from the processingdevice 140. In some embodiments, the terminal(s) 130 may be part of theprocessing device 140. In some embodiments, the terminal(s) 130 may beomitted.

The processing device 140 may process data and/or information obtainedfrom the MRI scanner 110, the terminal(s) 130, and/or the storage device150. For example, the processing device 140 may process MR signals ofone or more channels obtained from the MRI scanner 110 and reconstructan image of the subject. In some embodiments, the reconstructed imagemay be transmitted to the terminal(s) 130 and displayed on one or moredisplay devices in the terminal(s) 130. In some embodiments, theprocessing device 140 may be a single server, or a server group. Theserver group may be centralized, or distributed. In some embodiments,the processing device 140 may be local or remote. For example, theprocessing device 140 may access information and/or data stored in theMRI scanner 110, the terminal(s) 130, and/or the storage device 150 viathe network 120. As another example, the processing device 140 may bedirectly connected to the MRI scanner 110, the terminal(s) 130, and/orthe storage device 150 to access stored information and/or data. In someembodiments, the processing device 140 may be implemented on a cloudplatform. Merely by way of example, the cloud platform may include aprivate cloud, a public cloud, a hybrid cloud, a community cloud, adistributed cloud, an inter-cloud, a multi-cloud, or the like, or anycombination thereof. In some embodiments, the processing device 140 maybe implemented on a computing device 200 having one or more componentsillustrated in FIG. 2 in the present disclosure.

The storage device 150 may store data and/or instructions. In someembodiments, the storage device 150 may store data obtained from theterminal(s) 130 and/or the processing device 140. In some embodiments,the storage device 150 may store data and/or instructions that theprocessing device 140 may execute or use to perform exemplary methodsdescribed in the present disclosure. In some embodiments, the storagedevice 150 may include a mass storage device, a removable storagedevice, a volatile read-and-write memory, a read-only memory (ROM), orthe like, or any combination thereof. Exemplary mass storage may includea magnetic disk, an optical disk, a solid-state drive, etc. Exemplaryremovable storage may include a flash drive, a floppy disk, an opticaldisk, a memory card, a zip disk, a magnetic tape, etc. Exemplaryvolatile read-and-write memory may include a random access memory (RAM).Exemplary RAM may include a dynamic RAM (DRAM), a double date ratesynchronous dynamic RAM (DDR SDRAM), a static RAM (SRAM), a thyristorRAM (T-RAM), and a zero-capacitor RAM (Z-RAM), etc. Exemplary ROM mayinclude a mask ROM (MROM), a programmable ROM (PROM), an erasableprogrammable ROM (PEROM), an electrically erasable programmable ROM(EEPROM), a compact disk ROM (CD-ROM), and a digital versatile disk ROM,etc. In some embodiments, the storage device 150 may be implemented on acloud platform. Merely by way of example, the cloud platform may includea private cloud, a public cloud, a hybrid cloud, a community cloud, adistributed cloud, an inter-cloud, a multi-cloud, or the like, or anycombination thereof.

In some embodiments, the storage device 150 may be connected to thenetwork 120 to communicate with one or more components of the MRI system100 (e.g., the processing device 140, the terminal(s) 130, etc.). One ormore components of the MRI system 100 may access the data orinstructions stored in the storage device 150 via the network 120. Insome embodiments, the storage device 150 may be directly connected to orcommunicate with one or more components of the MRI system 100 (e.g., theprocessing device 140, the terminal(s) 130, etc.). In some embodiments,the storage device 150 may be part of the processing device 140.

FIG. 2 is a schematic diagram illustrating exemplary hardware and/orsoftware components of an exemplary computing device 200 on which theprocessing device 140 may be implemented according to some embodimentsof the present disclosure. As illustrated in FIG. 2, the computingdevice 200 may include a processor 210, a storage 220, an input/output(I/O) 230, and a communication port 240.

The processor 210 may execute computer instructions (program code) andperform functions of the processing device 140 in accordance withtechniques described herein. The computer instructions may include, forexample, routines, programs, objects, components, signals, datastructures, procedures, modules, and functions, which perform particularfunctions described herein. For example, the processor 210 may processdata obtained from the MRI scanner 110, the terminal(s) 130, the storagedevice 150, and/or any other component of the MRI system 100.Specifically, the processor 210 may process one or more measured datasets obtained from the MRI scanner 110. For example, the processor 210may perform one-dimensional (1D) correction or two-dimensional (2D)correction for the measured data set(s). The processor 210 mayreconstruct an image based on the corrected data set(s). In someembodiments, the reconstructed image may be stored in the storage device150, the storage 220, etc. In some embodiments, the reconstructed imagemay be displayed on a display device by the I/O 230. In someembodiments, the processor 210 may perform instructions obtained fromthe terminal(s) 130. In some embodiments, the processor 210 may includeone or more hardware processors, such as a microcontroller, amicroprocessor, a reduced instruction set computer (RISC), anapplication specific integrated circuits (ASICs), anapplication-specific instruction-set processor (ASIP), a centralprocessing unit (CPU), a graphics processing unit (GPU), a physicsprocessing unit (PPU), a microcontroller unit, a digital signalprocessor (DSP), a field programmable gate array (FPGA), an advancedRISC machine (ARM), a programmable logic device (PLD), any circuit orprocessor capable of executing one or more functions, or the like, orany combinations thereof.

Merely for illustration, only one processor is described in thecomputing device 200. However, it should be noted that the computingdevice 200 in the present disclosure may also include multipleprocessors, thus operations and/or method steps that are performed byone processor as described in the present disclosure may also be jointlyor separately performed by the multiple processors. For example, if inthe present disclosure the processor of the computing device 200executes both process A and process B, it should be understood thatprocess A and process B may also be performed by two or more differentprocessors jointly or separately in the computing device 200 (e.g., afirst processor executes process A and a second processor executesprocess B, or the first and second processors jointly execute processesA and B).

The storage 220 may store data/information obtained from the MRI scanner110, the terminal 130, the storage device 150, or any other component ofthe MRI system 100. In some embodiments, the storage 220 may include amass storage device, a removable storage device, a volatileread-and-write memory, a read-only memory (ROM), or the like, or anycombination thereof. For example, the mass storage may include amagnetic disk, an optical disk, a solid-state drive, etc. The removablestorage may include a flash drive, a floppy disk, an optical disk, amemory card, a zip disk, a magnetic tape, etc. The volatileread-and-write memory may include a random access memory (RAM). The RAMmay include a dynamic RAM (DRAM), a double date rate synchronous dynamicRAM (DDR SDRAM), a static RAM (SRAM), a thyristor RAM (T-RAM), and azero-capacitor RAM (Z-RAM), etc. The ROM may include a mask ROM (MROM),a programmable ROM (PROM), an erasable programmable ROM (PEROM), anelectrically erasable programmable ROM (EEPROM), a compact disk ROM(CD-ROM), and a digital versatile disk ROM, etc. In some embodiments,the storage 220 may store one or more programs and/or instructions toperform exemplary methods described in the present disclosure. Forexample, the storage 220 may store a program for the processing device140 for reducing or removing one or more artifacts in an image.

The I/O 230 may input or output signals, data, and/or information. Insome embodiments, the I/O 230 may enable a user interaction with theprocessing device 140. In some embodiments, the I/O 230 may include aninput device and an output device. Exemplary input devices may include akeyboard, a mouse, a touch screen, a microphone, or the like, or acombination thereof. Exemplary output devices may include a displaydevice, a loudspeaker, a printer, a projector, or the like, or acombination thereof. Exemplary display devices may include a liquidcrystal display (LCD), a light-emitting diode (LED)-based display, aflat panel display, a curved screen, a television device, a cathode raytube (CRT), or the like, or a combination thereof.

The communication port 240 may be connected to a network (e.g., thenetwork 120) to facilitate data communications. The communication port240 may establish connections between the processing device 140 and theMRI scanner 110, the terminal 130, or the storage device 150. Theconnection may be a wired connection, a wireless connection, orcombination of both that enables data transmission and reception. Thewired connection may include an electrical cable, an optical cable, atelephone wire, or the like, or any combination thereof. The wirelessconnection may include Bluetooth, Wi-Fi, WiMax, WLAN, ZigBee, mobilenetwork (e.g., 3G, 4G, 5G, etc.), or the like, or a combination thereof.In some embodiments, the communication port 240 may be a standardizedcommunication port, such as RS232, RS485, etc. In some embodiments, thecommunication port 240 may be a specially designed communication port.For example, the communication port 240 may be designed in accordancewith the digital imaging and communications in medicine (DICOM)protocol.

FIG. 3 is a schematic diagram illustrating exemplary hardware and/orsoftware components of an exemplary mobile device 300 according to someembodiments of the present disclosure. As illustrated in FIG. 3, themobile device 300 may include a communication platform 310, a display320, a graphic processing unit (GPU) 330, a central processing unit(CPU) 340, an I/O 350, a memory 360, and a storage 390. In someembodiments, any other suitable component, including but not limited toa system bus or a controller (not shown), may also be included in themobile device 300. In some embodiments, a mobile operating system 370(e.g., iOS, Android, Windows Phone, etc.) and one or more applications380 may be loaded into the memory 360 from the storage 390 in order tobe executed by the CPU 340. The applications 380 may include a browseror any other suitable mobile apps for receiving and renderinginformation relating to image processing or other information from theprocessing device 140. User interactions with the information stream maybe achieved via the I/O 350 and provided to the processing device 140and/or other components of the MRI system 100 via the network 120.

To implement various modules, units, and their functionalities describedin the present disclosure, computer hardware platforms may be used asthe hardware platform(s) for one or more of the elements describedherein. The hardware elements, operating systems and programminglanguages of such computers are conventional in nature, and it ispresumed that those skilled in the art are adequately familiar therewithto adapt those technologies to generate an image with reduced Nyquistghost artifact as described herein. A computer with user interfaceelements may be used to implement a personal computer (PC) or other typeof work station or terminal device, although a computer may also act asa server if appropriately programmed. It is believed that those skilledin the art are familiar with the structure, programming and generaloperation of such computer equipment and as a result the drawings shouldbe self-explanatory.

FIG. 4 is a block diagram illustrating an exemplary processing device140 according to some embodiments of the present disclosure. Theprocessing device 140 may be implemented on the computing device 200(e.g., the processor 210) illustrated in FIG. 2. The processing device140 may include a data acquisition module 410, a data pre-processingmodule 420, a data correction module 430, and an image reconstructionmodule 440.

The data acquisition module 410 may be configured to acquire image data.In some embodiments, the data acquisition module 410 may acquire theimage data (e.g., MR data) from the MRI scanner 110, the storage device150, the terminal(s) 130, and/or an external data source (not shown). Insome embodiments, the image data may include one or more measured datasets generated by echo planar imaging (EPI). In some embodiments, thedata acquisition module 410 may acquire instructions for processing themeasured data sets, or the like, or a combination thereof. In someembodiments, one or more radio frequency (RF) coils may be used for EPI.An RF coil may correspond to a channel. The RF coil(s) may receive thecorresponding channel(s) of MR signal(s). A measured data set maycorrespond to a channel of MR signal received by an RF coil. In someembodiments, the measured data set(s) may be filled (or entered) into adata space (e.g., k-space) in a roundabout manner. The filled k-spacemay include one or more k-space data sets corresponding to the measureddata set(s). The k-space data set(s) may include data corresponding toodd echoes and even echoes (see FIGS. 7A and 7B). In some embodiments, ameasured data set may be and/or include a full k-space data set, i.e.,the k-space data may be fully acquired. In some embodiments, a measureddata set may be and/or include a partially filled k-space data set,i.e., the k-space data may be partially acquired. In some embodiments,the acquired instructions may be executed by the processor(s) of theprocessing device 140 to perform exemplary methods described in thisdisclosure. In some embodiments, the acquired data may be transmitted tothe storage 200, the storage 390, the memory 360, etc. to be stored.

The data pre-processing module 420 may be configured to perform apreliminary correction for the measured data set(s) to generate one ormore pre-processed data sets. A pre-processed data set may correspond toa measured data set. In some embodiments, the measured data set(s) maybe preliminarily corrected in sequence to generate the pre-processeddata set(s). Alternatively or additionally, the measured data set(s) maybe preliminarily corrected simultaneously or synchronously to generatethe pre-processed data set(s). In some embodiments, the preliminarycorrection may include a one-dimensional (1D) correction and/or atwo-dimensional (2D) correction. The data pre-processing module 420 maypreliminarily correct the measured data set(s) based on one or morecorrection algorithms, for example, a reference correction algorithm(i.e., correction based on a reference scan), an iteration correction(e.g., iterative phase cycling), etc.

Merely by way of example, the data pre-processing module 420 maypreliminarily correct the measured data set(s) based on one or morereference data sets (e.g., reference echoes obtained by the dataacquisition module 410). In some embodiments, the reference echoes maybe detected without phase encoding. The data pre-processing module 420may determine one or more correction parameters based on the referenceecho(es). The correction parameter(s) may include phase deviation(s),phase deflection(s), phase offset(s), etc. The correction parameter(s)may be determined based on the phase differences between the referenceechoes. Then the data pre-processing module 420 may preliminarilycorrect the measured data set(s) based on the correction parameter(s).More descriptions of the data correction may be found elsewhere in thepresent disclosure. See, for example, FIG. 8 and the descriptionthereof.

The data correction module 430 may be configured to correct the measureddata set(s) or pre-processed data set(s). The data correction module 430may eliminate one or more phase inconsistencies of the measured dataset(s) or pre-processed data set(s). In some embodiments, the datacorrection module 430 may generate one or more data sets that includereduced or no phase inconsistency. In some embodiments, the datacorrection module 430 may update the generated data sets. In someembodiments, the data correction module 430 may generate the data setsbased on the pre-processed data set(s) or the measured data set(s). Thegenerated data set(s) may be different from the pre-processed dataset(s) or the measured data set(s). The generated data set(s) mayinclude combined data set(s). A combined data set may refer to a dataset obtained by combining two or more known data sets or previouslygenerated data sets. The data correction module 430 may generate acombined data set by combining two or more of a pre-processed data set,a measured data set, a synthetic data set generated based on one or morepre-processed data sets or measured data sets, or the like, or anycombination thereof.

In some embodiments, the data correction module 430 may generate thecombined data set(s) based on the pre-processed data set(s) or themeasured data set(s) by performing one or more iteration(s). Theiteration(s) may be terminated if the combined data set(s) satisfies oneor more conditions (also referred to as termination criteria), and thus,the combined data set(s) may be determined. In some embodiments, thecondition(s) may relate to a difference between the combined data setsgenerated in two consecutive iterations including a previous iterationand a current iteration. In response to the determination that thedifference is greater than a first threshold, the data correction module430 may determine to perform a next iteration. In response to thedetermination that the difference is lower than or equal to the firstthreshold, the data correction module 430 may determine to terminate theiteration(s). Then the combined data set(s) may be determined. In someembodiments, the condition(s) may relate to an iteration countrepresenting the number of iterations that have been performed. Inresponse to the determination that the iteration count is lower than asecond threshold, the data correction module 430 may determine toperform a next iteration. In response to the determination that theiteration count is greater than or equal to the second threshold, thedata correction module 430 may determine to terminate the iteration(s).Then the combined data set(s) may be determined. In some embodiments,the data correction module 430 may generate one or more convolutionkernels, one or more synthetic data sets, etc. More description of thedata correction module 430 can be found in connection with FIG. 5, andis not repeated here.

The image reconstruction module 440 may be configured to reconstruct oneor more images. In some embodiments, the image reconstruction module 440may reconstruct the image(s) based on one or more data sets (e.g., themeasured data set(s), the pre-processed data set(s), and/or the combineddata set(s)). The image reconstruction module 440 may reconstruct theimage(s) based on a Fourier transform technique and/or one or more datafilling techniques.

If the data set(s) (e.g., the measured data set(s), the pre-processeddata set(s), and/or the combined data set(s)) are full k-space dataset(s), the image reconstruction module 440 may reconstruct the image(s)according to a technique based on Fourier transform. The imagereconstruction module 440 may process the data set(s) with an inverseFourier transform to generate the image(s). Merely by way of example,the image reconstruction module 440 may perform an inverse Fouriertransform for one of the data sets to generate a sub image. Thus, aplurality of sub images may be generated based on the data sets. A dataset and the resultant sub image may correspond to a channel. The imagereconstruction module 440 may generate an image by combining the subimages using a reconstruction technique. Exemplary reconstructiontechniques may include “Sum of Squares” (SoS) reconstruction, optimalarray reconstruction, etc. In some embodiments, the image reconstructionmodule 440 may determine one or more weights (or weighting factors) forthe data set(s). The weight(s) of the data set(s) may be the same ordifferent. The image reconstruction module 440 may combine the dataset(s) based on the weight(s) to generate a reconstructed data set. Theimage reconstruction module 440 may perform an inverse Fourier transformfor the reconstructed data set to obtain a reconstructed image.

If the data set(s) (e.g., the measured data set(s), the pre-processeddata set(s), and/or the combined data set(s)) are partially filledk-space data set(s), the image reconstruction module 440 may reconstructthe image(s) according to a technique based on Fourier transform incombination with one or more data filling techniques. In someembodiments, the image reconstruction module 440 may reconstruct a fullk-space data set by filling each of the partially filled k-space dataset(s). Exemplary data filling techniques may include simultaneousacquisition of spatial harmonics (SMASH), AUTO-SMASH, VD (variabledensity)-AUTO-SMASH, sensitivity encoding (SENSE), modified SENSE(mSENSE), parallel imaging with localized sensitivities (PILS),generalized auto-calibrating partially parallel acquisitions (GRAPPA),iterative self-consistent parallel imaging reconstruction (SPIRiT), etc.Then the image reconstruction module 440 may process the full k-spacedata set with an inverse Fourier transform to generate an image. In someembodiments, the image reconstruction module 440 may process one fullk-space data set corresponding to a channel with an inverse Fouriertransform to generate one sub image. Thus, a plurality of sub images maybe generated based on a plurality of full k-space data setscorresponding to the plurality of data sets. The image reconstructionmodule 440 may generate an image by combining the sub images using areconstruction technique. Exemplary reconstruction techniques mayinclude SoS reconstruction, optimal array reconstruction, etc.

It should be noted that the above description of the processing engineis provided for the purposes of illustration, and is not intended tolimit the scope of the present disclosure. For persons having ordinaryskills in the art, multiple variations and modifications may be madeunder the teachings of the present disclosure. However, those variationsand modifications do not depart from the scope of the presentdisclosure. For example, the data pre-processing module 420 and the datacorrection module 430 may be integrated into one module configured toperform a preliminary correction on the measured data set(s) andgenerate one or more combined data sets. In some embodiments, one ormore of the modules may be installed on a different device separatedfrom the other modules. Merely by way of example, the imagereconstruction module 440 may reside in a device, and other modules mayreside on a different device.

FIG. 5 is a block diagram illustrating an exemplary data correctionmodule 430 according to some embodiments of the present disclosure. Thedata correction module 430 may be implemented on the computing device200 (e.g., the processor 210) illustrated in FIG. 2. The data correctionmodule 430 may include a convolution kernel determination unit 502, asynthetic data generation unit 504, a combined data generation unit 506,a data updating unit 508, and a judgment unit 510.

The convolution kernel determination unit 502 may be configured todetermine one or more convolution kernels based on the measured dataset(s) or pre-processed data set(s). In some embodiments, the number ofconvolution kernels may relate to the number of measured data set(s) orpre-processed data set(s) or the number of channels. In someembodiments, the convolution kernel determination unit 502 may determineone convolution kernel for a corresponding data set (e.g., a measureddata set or pre-processed data set) or a corresponding channel. Merelyby way of example, if there are 9 channels (i.e., 9 corresponding datasets), the convolution kernel determination unit 502 may determine 9convolution kernels. In some embodiments, the convolution kerneldetermination unit 502 may determine one convolution kernel based on oneor more of the corresponding data sets. For example, the convolutionkernel determination unit 502 may determine a first convolution kernelfor a first channel based on the data sets obtained from the firstchannel and one or more other channels (e.g., from all the channels). Asanother example, the convolution kernel determination unit 502 maydetermine a second convolution kernel for a second channel based on thedata sets obtained from the second channel and one or more otherchannels (e.g., from all the channels). In some embodiments, theconvolution kernels for multiple channels or corresponding data sets maybe the same or different from each other.

A convolution kernel may refer to a matrix of a certain size thatincludes one or more elements. In some embodiments, a convolution kernelmay be expressed as a data matrix with kx dimension (see FIG. 10B), kydimension (see FIG. 10B), and/or a channel dimension. The range of aconvolution kernel within the three dimensions (kx dimension, kydimension, and the channel dimension) may be also referred to as asupporting range. The size of the convolution kernel may correspond tothe size of the data matrix. The size of a convolution kernel may bedetermined based on the number of data points of a corresponding dataset (e.g., a corresponding measured data set or pre-processed data set)and/or the number of channels. As the number of channels may be alreadyknown, the channel dimension of a convolution kernel may not bepresented in the dimensions for brevity in the present disclosure. Forexample, a convolution kernel with a M×N×C matrix may be expressed as aM×N matrix for simplicity, wherein M is kx dimension, N is ky dimension,C is the number of channels, and the M×N matrix is referred to as theM×N×C matrix. In some embodiments, a convolution kernel may have asquare shape, a rectangular shape, a triangular shape, an ellipticalshape, a cuboid shape, a cylindrical shape, a hexagonal shape, etc.Merely by way of example, for a convolution kernel with a square shapefor each channel, the convolution kernel may be a 3×3 matrix, a 5×5matrix, etc. As another example, for a convolution kernel with arectangular shape for each channel, the convolution kernel may be a 3×5matrix, a 5×6 matrix, etc. In some embodiments, a convolution kernel maynot have to include all surrounding data points. For example, aconvolution kernel with a hexagonal shape for each channel may notinclude one or more data points surrounding the supporting range of thehexagonal shape. It should be noted that a data set (e.g., a measureddata set, a pre-processed data set, a synthetic data set, a combineddata set, etc.) described in the present disclosure may be expressed asa data matrix.

In some embodiments, the convolution kernel determination unit 502 maydetermine the convolution kernel(s) in k-space. Alternatively oradditionally, the convolution kernel determination unit 502 maydetermine the convolution kernel(s) in an intermediate space. Theintermediate space may be a data space between k-space and an imagespace. In some embodiments, the intermediate space may be determined byprocessing k-space with a 1D inverse Fourier transform.

In some embodiments, the convolution kernel determination unit 502 maygenerate a convolution kernel based on a portion of one or morecorresponding data sets (e.g., all the corresponding data sets). In someembodiments, the portion of corresponding data sets may be located atany position of the corresponding data sets (e.g., a central region, aregion close to an edge of the corresponding data sets). In someembodiments, all the corresponding data sets may be used to generate aconvolution kernel. In some embodiments, the values for one or moreelements of a convolution kernel may be determined by sliding theconvolution kernel in k-space (or an intermediate space) and fit eachtarget point (see, e.g., point T in FIG. 10A) using data points withinthe supporting range. A target point may refer to a known point (e.g., aknown point in the measured (or pre-processed) data set(s)) at thecenter of the supporting range. In some embodiments, if at least onecorresponding data set (e.g., a corresponding measured data set or thepre-processed data set) is or includes a partially filled k-space dataset, the convolution kernel determination unit 502 may generate aconvolution kernel based on a region including relatively dense datafrom the partially filled k-space data. In some embodiments, if thepartially filled k-space data are not evenly distributed and arelatively dense area exists, the convolution kernel determination unit502 may generate a convolution kernel based on the relatively dense areain the partially filled k-space data set. As used herein, “a regionincluding relatively dense data” may indicate that the region includesan area that is filled with a larger amount of k-space data than anotherregion of the partially filled k-space. For example, if an accelerationfactor is 2 and the filled k-space data are not evenly distributed, theconvolution kernel determination unit 502 may select a matrix containingrelatively dense k-space data along the readout direction and the phaseencoding direction. The acceleration factor may relate to a datasampling rate. For example, if the acceleration factor is 2, only halfdata may be sampled, and accordingly the sampling time may be halved. Asused herein, that partially filled k-space data are evenly distributedmay indicate that the ky intervals (i.e., the intervals in the kydirection) between the odd echoes and/or the even echoes correspondingto the partially filled k-space data are substantially the same. Forevenly distributed data, the difference between a first ky interval anda second ky interval between the odd echoes and/or the even echoescorresponding to the partially filled k-space data may be less than athreshold relating to the ky interval. As used herein, that partiallyfilled k-space data are not evenly distributed may indicate that the kyintervals between the odd echoes and/or the even echoes corresponding tothe partially filled k-space data are substantially not the same. Fornon-evenly distributed data, the difference between a first ky intervaland a second ky interval between the odd echoes and/or the even echoescorresponding to the partially filled k-space data may be no less than athreshold relating to the ky interval. Specifically, the convolutionkernel may be generated by data fitting based on a kernel function andone or more data points of the corresponding data sets. Moredescriptions of the kernel function may be found elsewhere in thepresent disclosure. See, for example, Equation (1) and the descriptionthereof.

The synthetic data generation unit 504 may be configured to generate oneor more synthetic data sets. A synthetic data set may refer to a dataset synthesized based on one or more known data sets (e.g., the measureddata set(s), the pre-processed data set(s), the combined data set(s),etc.) or previously generated data sets. In some embodiments, thesynthetic data generation unit 504 may generate a synthetic data setbased on a convolution kernel and one or more corresponding data sets(e.g., all the measured data sets or pre-processed data sets). Forexample, the synthetic data generation unit 504 may generate a syntheticdata set by traversing the corresponding data set(s) (e.g., all themeasured data sets or pre-processed data sets) using a convolutionkernel. In some embodiments, if there are multiple channels (i.e.,multiple corresponding data sets), the synthetic data generation unit504 may generate multiple synthetic data sets. For example, if there are9 channels (i.e., 9 corresponding data sets), the synthetic datageneration unit 504 may generate 9 synthetic data sets, in which eachsynthetic data set may be generated based on a convolution kernel andall the 9 corresponding data sets (e.g., all the measured data sets orpre-processed data sets). In some embodiments, the synthetic datageneration unit 504 may generate multiple synthetic data setssimultaneously, or in sequence. In some embodiments, the synthetic datageneration unit 504 may generate the synthetic data set(s) in k-space orthe intermediate space. It should be noted that the synthetic datageneration unit 504 may not fill a data set or increase the amount ofdata in a corresponding synthetic data set. For example, if a measureddata set or a pre-processed data set includes a full k-space data set, acorresponding synthetic data set may be a substantially full k-spacedata set. As another example, if a measured data set or a pre-processeddata set includes a partially filled k-space data set, a correspondingsynthetic data set may still be a partially filled k-space data set.

The combined data generation unit 506 may be configured to generate oneor more combined data sets. In some embodiments, the combined datageneration unit 506 may generate a combined data set based on two ormore known data sets. For example, the combined data generation unit 506may generate a combined data set based on a synthetic data set and ameasured (or pre-processed) data set. In some embodiments, the combineddata generation unit 506 may generate multiple combined data sets basedon multiple synthetic data sets and multiple measured (or pre-processed)data sets, in which each combined data set may relate to one of thesynthetic data set(s) and the corresponding measured (or pre-processed)data set(s).

In some embodiments, the combined data generation unit 506 may generatethe combined data set(s) based on one or more weighting factors (orweights). For example, the combined data generation unit 506 maydetermine a weighted sum of a synthetic data set and a correspondingmeasured (or pre-processed) data set based on the weighting factor(s).The combined data generation unit 506 may designate the weighted sum asa combined data set. In some embodiments, the weighting factor(s) fordifferent combined data sets may be the same or different. It should benoted that the combined data generation unit 506 may generate thecombined data set(s) based on one or more other algorithms, such as arelaxation iteration, an optimization algorithm, etc. The combined datageneration unit 506 may generate the combined data set(s) in k-space orthe intermediate space. If a synthetic data set includes a full k-spacedata set, the corresponding combined data set may still be a fullk-space data set. If a synthetic data set includes partially filledk-space data set, the corresponding combined data set may still be apartially filled k-space data set.

The data updating unit 508 may be configured to update the convolutionkernel(s) determined by the convolution kernel determination unit 502,the synthetic data set(s) generated by the synthetic data generationunit 504, and/or the combined data set(s) generated by the combined datageneration unit 506 in one or more iterations. Merely by way of example,the data updating unit 508 may update the convolution kernel(s) in aniteration, update the synthetic data set(s) based on the updatedconvolution kernel(s), and then update the combined data set(s) based onthe updated synthetic data set(s). In some embodiments, the dataupdating unit 508 may update the measured data set(s) or thepre-processed data set(s). For example, the data updating unit 508 maydesignate the combined data set(s) as the measured data set(s) or thepre-processed data set(s), and then update the convolution kernel(s)based on the updated measured data set(s) or the pre-processed dataset(s). In some embodiments, the data updating unit 508 may update oneor more parameters relating to an iteration algorithm, for example, aniteration count, time spent for iteration, etc. Merely by way ofexample, the data updating unit 508 may update an iteration count bycounting the number of current iterations that have been performed.

The judgment unit 510 may be configured to determine whether thecombined data set(s) satisfy a condition. In some embodiments, thecondition may relate to the difference between the combined data setsgenerated in two or more consecutive iterations. The judgment unit 510may determine whether the difference is greater than a first threshold.In some embodiments, in response to the determination that thedifference is greater than the first threshold, the judgment unit 510may determine to perform a next iteration. In some embodiments, inresponse to the determination that the difference is lower than or equalto the first threshold, the judgment unit 510 may determine to terminatethe iteration(s). In some embodiments, the condition may relate to aniteration count representing the number of iterations that have beenperformed. The judgment unit 510 may determine whether the iterationcount is greater than a second threshold. In response to thedetermination that the iteration count is lower than the secondthreshold, the judgment unit 510 may determine to perform a nextiteration. In response to the determination that the iteration count isgreater than or equal to the second threshold, the judgment unit 510 maydetermine to terminate the iteration(s). In some embodiments, the firstthreshold and/or the second threshold may be predetermined according topractical scenarios. The first threshold and/or the second threshold maybe part of default settings of the processing device 140, or may be setor adjusted by a user (e.g., a doctor).

FIG. 6 is a flowchart illustrating an exemplary process 600 forgenerating an image with reduced or no Nyquist ghost artifact accordingto some embodiments of the present disclosure. In some embodiments, oneor more operations of process 600 illustrated in FIG. 6 for generatingan image with reduced Nyquist ghost artifact may be implemented in theMRI system 100 illustrated in FIG. 1. For example, the process 600illustrated in FIG. 6 may be stored in the storage device 150 in theform of instructions, and invoked and/or executed by the processingdevice 140 (e.g., the processor 210 of the computing device 200 asillustrated in FIG. 2, the CPU 340 of the mobile device 300 asillustrated in FIG. 3). As another example, a portion of the process 600may be implemented on the MRI scanner 110. The operations of theillustrated process presented below are intended to be illustrative. Insome embodiments, the process may be accomplished with one or moreadditional operations not described, and/or without one or more of theoperations discussed. Additionally, the order in which the operations ofthe process as illustrated in FIG. 6 and described below is not intendedto be limiting.

In 610, one or more measured data sets may be obtained. The operation610 may be performed by the data acquisition module 410. In someembodiments, the measured data sets may be generated by echo planarimaging (EPI). EPI is a bi-polar readout scan technique. In someembodiments, one or more radiofrequency (RF) coils may be used for EPI.An RF coil may correspond to a channel. An EPI scan may produce a trainor series of gradient echoes (also referred to as successive MRsignals). The RF coil(s) may receive MR signal(s) from the correspondingchannel(s). A measured data set may correspond to an MR signal from achannel received by an RF coil. The measured data set(s) may be filledin a data space (e.g., k-space) in a roundabout manner. The filledk-space may include one or more k-space data sets corresponding to themeasured data set(s). The k-space data set(s) may include datacorresponding to one or more odd echoes and one or more even echoes (asshown in FIGS. 7A and 7B). In some embodiments, a measured data set maybe and/or include a full k-space data set, i.e., the k-space data may befully acquired (or filled) by way of sampling, data filling, etc. Insome embodiments, a measured data set may be and/or include a partiallyfilled k-space data set, i.e., the k-space data may be partiallyacquired (or filled).

In 620, a preliminary correction may be performed for the measured dataset(s) obtained in 610 to generate one or more pre-processed data sets.The operation 620 may be performed by the data pre-processing module420. A pre-processed data set may correspond to a measured data set. Insome embodiments, multiple measured data sets may be corrected insequence to generate the pre-processed data set(s). Alternatively oradditionally, multiple measured data sets may be correctedsimultaneously or synchronously to generate the pre-processed dataset(s). In some embodiments, the preliminary correction may include a 1Dcorrection and/or a 2D correction. An exemplary preliminary correctionis described in connection with FIG. 8, and is not repeated here. Insome embodiments, operation 620 may be omitted. Thus, the measured dataset(s) without preliminary correction may be used for further processing(e.g., for generating one or more combined data sets).

In 630, one or more combined data sets may be generated based on thepre-processed data set(s) or the measured data set(s). The operation 630may be performed by the data correction module 430. A combined data setmay relate to a corresponding pre-processed data set or a correspondingmeasured data set. In some embodiments, the combined data set(s) may begenerated by performing one or more iterations based on thepre-processed data set(s) or the measured data set(s). In someembodiments, the combined data set(s) may be updated in theiteration(s). The iteration(s) are described in detail in connectionwith FIG. 9, and are not repeated here. The iteration(s) may beterminated if the combined data set(s) satisfy one or more conditions,and the combined data set(s) may be determined. In some embodiments, thecondition(s) may relate to a difference between the combined data setsgenerated in two or more consecutive iterations. In response to thedetermination that the difference is greater than a first threshold, thedata correction module 430 may determine to perform a next iteration. Inresponse to the determination that the difference is lower than or equalto the first threshold, the data correction module 430 may determine toterminate the iteration(s). Then the combined data set(s) may bedetermined. In some embodiments, the condition(s) may relate to aniteration count representing the number of iterations that have beenperformed. In response to the determination that the iteration count islower than a second threshold, the data correction module 430 maydetermine to perform a next iteration. In response to the determinationthat the iteration count is greater than or equal to a second threshold,the data correction module 430 may determine to terminate theiteration(s). Then the combined data set(s) may be determined. The firstthreshold and/or the second threshold may be predetermined according topractical scenarios. The first threshold and/or the second threshold maybe part of default settings of the processing device 140, or may be setor adjusted by a user (e.g., a doctor).

In 640, an image may be reconstructed based on the combined data set(s).The operation 640 may be performed by the image reconstruction module440. In some embodiments, the image may be reconstructed according to atechnique based on Fourier transform and/or one or more data fillingtechniques.

If the combined data set(s) are full k-space data set(s), the image maybe reconstructed according to a technique based on Fourier transform.The combined data set(s) may be processed with an inverse Fouriertransform to generate the image. In some embodiments, one of thecombined data sets may be processed with an inverse Fourier transform togenerate a sub image. Thus, a plurality of sub images may be generatedbased on the combined data sets. A combined data set and the resultantsub image may correspond to a channel. Then an image may be generated bycombining the sub images using a reconstruction technique. Exemplaryreconstruction techniques may include “Sum of Squares” (SoS)reconstruction, optimal array reconstruction, etc. In some embodiments,the image reconstruction module 440 may determine one or more weights(or weighting factors) for the combined data set(s). The weight(s) ofthe combined data set(s) may be the same or different. The imagereconstruction module 440 may combine the combined data set(s) based onthe weight(s) to generate a reconstructed data set. The imagereconstruction module 440 may perform an inverse Fourier transform forthe reconstructed data set to obtain a reconstructed image.

If the combined data set(s) are partially filled k-space data set(s),the image reconstruction module 440 may reconstruct an image accordingto a technique based on Fourier transform in combination with one ormore data filling techniques. In some embodiments, the imagereconstruction module 440 may reconstruct a full k-space data set byfilling each of the combined data set(s) (or partially filled k-spacedata set(s)). Exemplary data filling techniques may include simultaneousacquisition of spatial harmonics (SMASH), AUTO-SMASH, VD (variabledensity)-AUTO-SMASH, sensitivity encoding (SENSE), modified SENSE(mSENSE), parallel imaging with localized sensitivities (PILS),generalized auto-calibrating partially parallel acquisitions (GRAPPA),iterative self-consistent parallel imaging reconstruction (SPIRiT), etc.Then the image reconstruction module 440 may process the full k-spacedata set with an inverse Fourier transform to generate an image. In someembodiments, the image reconstruction module 440 may process one fullk-space data set corresponding to a channel with an inverse Fouriertransform to generate one sub image. Thus, a plurality of sub images maybe generated based on a plurality of full k-space data setscorresponding to the plurality of combined data sets. The imagereconstruction module 440 may generate an image by combining the subimages using a reconstruction technique. Exemplary reconstructiontechniques may include SoS reconstruction, optimal array reconstruction,etc.

It should be noted that the above description of the process forgenerating an image with reduced or no Nyquist ghost artifact isprovided for the purposes of illustration, and is not intended to limitthe scope of the present disclosure. For persons having ordinary skillsin the art, multiple variations and modifications may be made under theteachings of the present disclosure. However, those variations andmodifications do not depart from the scope of the present disclosure. Insome embodiments, k-space may be processed with a one-dimensional (1D)inverse Fourier transform to determine an intermediate space. Theintermediate space may be between k-space and an image space. Thek-space data set(s) may be processed with the 1D inverse Fouriertransform to generate one or more intermediate space data set(s). Theintermediate space data set(s) may correspond to the k-space dataset(s). The intermediate space data set(s) may be used for processing togenerate an image with reduced or no Nyquist ghost artifact.

In some embodiments, another exemplary process for generating an image(e.g., an MR image) may include one or more of the following operations.A plurality of magnetic resonance (MR) signals may be generated byscanning a subject using an imaging device (e.g., an MR imaging device).The plurality of MR signals may be received using a plurality ofradiofrequency (RF) coils of the imaging device. A plurality of measuredk-space data sets may be obtained by entering (also referred to asfilling) the MR signals into k-space, wherein each measured k-space dataset may correspond to one of the plurality of RF coils. One or morecorrections may be performed for the plurality of measured k-space datasets to obtain a plurality of corrected k-space data sets. An imagerelated to the subject may be reconstructed based on the plurality ofcorrected k-space data sets. In some embodiments, the one or morecorrections may include one or more of the following operations. Aplurality of convolution kernels may be determined based on theplurality of measured k-space data sets (see, e.g., operation 901). Aplurality of synthetic k-space data sets may be generated based on theplurality of convolution kernels and the plurality of measured k-spacedata sets (see, e.g., operation 903). The plurality of corrected k-spacedata sets may be generated based on the plurality of synthetic k-spacedata sets and the plurality of measured k-space data sets (see, e.g.,operation 905). In some embodiments, before determining the plurality ofconvolution kernels, a linear or non-linear correction (e.g., a linearor non-linear preliminary correction) may be performed for the pluralityof measured k-space data sets. The linear or non-linear correction maybe any 1D correction or 2D correction described in the presentdisclosure. In some embodiments, the determination of the plurality ofconvolution kernels may include one or more of the following operations.The plurality of measured k-space data sets may be processed withone-dimensional (1D) inverse Fourier transform to obtain an intermediateimage. The plurality of convolution kernels may be determined based onthe intermediate image. In some embodiments, the intermediate image maybe an image correspond to the data in an intermediate space.

FIGS. 7A and 7B are schematic diagrams illustrating exemplary echoesfilled into k-space according to some embodiments of the presentdisclosure. FIG. 7A shows ideal echoes filled in k-space. As shown inFIG. 7A, there may be no inconsistencies between echoes (e.g., echo 1through echo 7). Specifically, the echoes (e.g., echo 1 through echo 7)may have the same eddy current induced phase (e.g., ϕ) and delays alongboth the readout direction (Kx) and phase encoding direction (Ky).Accordingly, an image reconstructed based on the k-space data shown inFIG. 7A may include no Nyquist ghost artifact.

FIG. 7B shows echoes filled in k-space that include inconsistencies. Insome embodiments, the echoes shown in FIG. 7B may be generated by EPI.EPI is a bi-polar readout scan technique. A gradient pulse sequence maybe used for an EPI scan. A gradient pulse sequence may include a trainof gradient pulses of continually alternating polarities in the readoutdirection (i.e., Kx direction in FIG. 7B), and a train of gradientpulses in the phase encoding direction (i.e., Ky direction in FIG. 7B).The EPI scan may produce a corresponding train or series of gradientechoes (also referred to as successive MR signals). The echoes may bedesignated as “odd” (e.g., echo 1, echo 3, echo 5, and echo 7 in FIG.7B) or “even” (e.g., echo 2, echo 4, and echo 6 in FIG. 7B) based ontheir respective positions in the echo train. The odd echoes and theeven echoes may be acquired with opposite readout gradient polarities,respectively. Accordingly, MR data corresponding to the MR signals maybe filled into k-space in a roundabout manner, and roundabout echoes maybe generated in k-space. However, due to eddy current induced by thehigh-speed switching of a gradient magnetic field with differentpolarities, a shift, etc., inconsistencies between the odd echoes andthe even echoes may be generated. The inconsistencies in k-space datamay in turn lead to Nyquist ghost artifact in a reconstructed image. Asshown in FIG. 7B, the inconsistencies may include different phases(e.g., ϕ₁ and ϕ₂), delay along the readout direction (e.g., ΔKx), andshift along the phase encoding direction (e.g., ΔKy). In someembodiments, the different phases and delay along the Kx direction maybe corrected at least to some extent by performing a one-dimensional(1D) correction. However, there may still be artifact in a reconstructedimage (as shown in FIGS. 11A and 11B). A two-dimensional (2D) correctionmay be performed to reduce or remove the Nyquist ghost artifact. The 2Dcorrection technique described in the present disclosure (see, e.g.,FIGS. 6 and 9) may substantially eliminate Nyquist ghost artifact (asshown in FIGS. 11C and 11D). It should be noted that the 2D correctiontechnique described in the present disclosure may eliminate or reducethe phase differences between even echoes and odd echoes without usingextra calibration data or reference data.

It should be noted that the above illustrated echoes in k-space isprovided for the purposes of illustration, and is not intended to limitthe scope of the present disclosure. For persons having ordinary skillsin the art, multiple variations and modifications may be made under theteachings of the present disclosure. However, those variations andmodifications do not depart from the scope of the present disclosure.For example, the echoes may only include differences along the readoutdirection.

FIG. 8 is a flowchart illustrating an exemplary process 800 forperforming a preliminary correction for measured data set(s) accordingto some embodiments of the present disclosure. In some embodiments, oneor more operations of process 800 illustrated in FIG. 8 for performing apreliminary correction may be implemented in the MRI system 100illustrated in FIG. 1. For example, the process 800 illustrated in FIG.8 may be stored in the storage device 150 in the form of instructions,and invoked and/or executed by the processing device 140 (e.g., theprocessor 210 of the computing device 200 as illustrated in FIG. 2, theCPU 340 of the mobile device 300 as illustrated in FIG. 3). As anotherexample, a portion of the process 800 may be implemented on the MRIscanner 110. In some embodiments, operation 620 illustrated in FIG. 6may be performed according to process 800. The operations of theillustrated process presented below are intended to be illustrative. Insome embodiments, the process may be accomplished with one or moreadditional operations not described, and/or without one or more of theoperations discussed. Additionally, the order in which the operations ofthe process as illustrated in FIG. 8 and described below is not intendedto be limiting.

In some embodiments, the preliminary correction may include aone-dimensional (1D) correction for reducing inconsistencies betweenodd-even echoes. Generally, the 1D correction may correct phase anddelay along the readout direction (e.g., different phases ϕ₁ and ϕ₂, andΔKx in FIG. 7B). After the 1D correction, the pre-processed data set(s)may be used for generating the combined data set(s). Merely by way ofexample, a 1D correction technique is described below.

In 801, one or more reference echoes may be obtained. The operation 801may be performed by the data pre-processing module 420. In someembodiments, the data pre-processing module 420 may obtain data relatingto the reference echoes via the data acquisition module 410. Thereference echo(es) may be echoes detected without phase encoding. Insome embodiments, the number of the reference echo(es) may be three,including two even echoes and an odd echo (e.g., a first even echo, asecond odd echo, and a third even echo). In some embodiments, the numberof the reference echo(es) may be four, including two even echoes and twoodd echoes.

In 803, one or more correction parameters may be determined based on thereference echo(es) obtained in 801. The operation 803 may be performedby the data pre-processing module 420. The correction parameter(s) mayrelate to one or more phase deviations, one or more phase deflections,one or more phase offsets, etc., of the reference echo(es). Thecorrection parameter(s) may be determined based on phase differences ofthe reference echo(es) after 1D inverse Fourier transform along thereadout direction. For example, if the number of the reference echo(es)is three, the phase difference may refer to a phase difference betweenan even echo and an odd echo (e.g., a first even echo and a second oddecho, a second odd echo and a third even echo). In some embodiments, thedata pre-processing module 420 may perform a 1D inverse Fouriertransform for the reference echo(es) along the readout direction. Thedata pre-processing module 420 may determine the phase differences ofthe transformed reference echo(es).

In 805, the measured data set(s) may be corrected based on thecorrection parameter(s) determined in 803. The operation 805 may beperformed by the data pre-processing module 420. In some embodiments,the data pre-processing module 420 may perform a 1D inverse Fouriertransform for the measured data set(s) along the readout direction togenerate one or more intermediate data sets. The data pre-processingmodule 420 may correct the intermediate data set(s) based on thecorrection parameter(s).

It should be noted that the above description of the process 800 forperforming the 1D correction for the measured data set(s) is providedfor the purposes of illustration, and is not intended to limit the scopeof the present disclosure. For persons having ordinary skills in theart, multiple variations and modifications may be made under theteachings of the present disclosure. However, those variations andmodifications do not depart from the scope of the present disclosure. Insome embodiments, a fitting model may be determined based on thereference echoes and readout positions. The measured data set(s) may becorrected based on the fitting model. More descriptions of the 1Dcorrection may be found in, e.g., Chinese Patent Nos. 104035059 entitled“METHOD FOR RECONSTRUCTING IMAGE PRODUCED BY ECHO PLANAR IMAGINGSEQUENCE” filed Mar. 6, 2013, and 104865545 entitled “METHOD AND DEVICEFOR ECHO PLANAR IMAGING” filed Feb. 21, 2014, the contents of each ofwhich are hereby incorporated by reference.

FIG. 9 is a flowchart illustrating an exemplary process 900 forgenerating one or more combined data sets according to some embodimentsof the present disclosure. In some embodiments, one or more operationsof process 900 illustrated in FIG. 9 for generating combined data set(s)may be implemented in the MRI system 100 illustrated in FIG. 1. Forexample, the process 900 illustrated in FIG. 9 may be stored in thestorage device 150 in the form of instructions, and invoked and/orexecuted by the processing device 140 (e.g., the processor 210 of thecomputing device 200 as illustrated in FIG. 2, the CPU 340 of the mobiledevice 300 as illustrated in FIG. 3). As another example, a portion ofthe process 900 may be implemented on the MRI scanner 110. In someembodiments, operation 630 illustrated in FIG. 6 may be performedaccording to process 900. The operations of the illustrated processpresented below are intended to be illustrative. In some embodiments,the process may be accomplished with one or more additional operationsnot described, and/or without one or more of the operations discussed.Additionally, the order in which the operations of the process asillustrated in FIG. 9 and described below is not intended to belimiting.

In 901, one or more convolution kernels may be determined based on themeasured data set(s) obtained in 610 or the pre-processed data set(s)generated in 620. The operation 901 may be performed by the convolutionkernel determination unit 502. In some embodiments, the convolutionkernel(s) may be determined in k-space. Alternatively or additionally,the convolution kernel(s) may be determined in an intermediate spacebetween k-space and an image space. In some embodiments, the convolutionkernel determination unit 502 may determine one convolution kernel for acorresponding data set (e.g., a measured data set or pre-processed dataset) or a corresponding channel. In some embodiments, each measured dataset or each pre-processed data set may have a corresponding convolutionkernel. Merely by way of example, if there are 9 channels (i.e., 9corresponding data sets), the convolution kernel determination unit 502may determine 9 convolution kernels. In some embodiments, theconvolution kernel determination unit 502 may determine one convolutionkernel based on one or more of the corresponding data sets (e.g., allthe 9 corresponding data sets or 9 channels). In some embodiments, eachconvolution kernel may relate to all of the measured data set(s) or thepre-processed data set(s). For example, the convolution kerneldetermination unit 502 may determine a first convolution kernel for afirst channel based on the data sets obtained from the first channel andone or more other channels (e.g., from all the channels). As anotherexample, the convolution kernel determination unit 502 may determine asecond convolution kernel for a second channel based on the data setsobtained from the second channel and one or more other channels (e.g.,from all the channels). In some embodiments, the convolution kernels formulti channels or corresponding data sets may be different from eachother. For example, the values of the elements of at least twoconvolution kernels may be different. As another example, the sizes ofat least two convolution kernels may be different. As a further example,the shapes of at least two convolution kernels may be different.

In some embodiments, the convolution kernel determination unit 502 maygenerate a convolution kernel based on a portion of one or morecorresponding data sets (e.g., all the corresponding data sets). In someembodiments, the portion of corresponding data sets may be located atany position of the corresponding data sets (e.g., a central region, aregion close to an edge of the corresponding data sets). In someembodiments, all the corresponding data sets may be used to generate aconvolution kernel. In some embodiments, the values for one or moreelements of a convolution kernel may be determined by sliding theconvolution kernel in k-space (or an intermediate space) and fit eachtarget point (see, e.g., point T in FIG. 10A) using data points withinthe supporting range. A target point may refer to a known point (e.g., aknown point in the measured (or pre-processed) data set(s)) at thecenter of the supporting range. In some embodiments, if at least onecorresponding data set (e.g., a corresponding measured data set or thepre-processed data set) is or includes a partially filled k-space dataset, the convolution kernel determination unit 502 may generate aconvolution kernel based on a region including relatively dense datafrom the partially filled k-space data. In some embodiments, if thepartially filled k-space data are not evenly distributed and arelatively dense area exists, the convolution kernel determination unit502 may generate a convolution kernel based on the relatively dense areain the partially filled k-space data set. As used herein, “a regionincluding relatively dense data” may indicate that the region includesan area that is filled with a larger amount of k-space data than anotherregion of the partially filled k-space. For example, if an accelerationfactor is 2 and the filled k-space data are not evenly distributed, theconvolution kernel determination unit 502 may select a matrix containingrelatively dense k-space data along the readout direction and the phaseencoding direction. The acceleration factor may relate to a datasampling rate. For example, if the acceleration factor is 2, only halfdata may be sampled, and accordingly the sampling time may be halved. Asused herein, that partially filled k-space data are evenly distributedmay indicate that the ky intervals (i.e., the intervals in the kydirection) between the odd echoes and/or the even echoes correspondingto the partially filled k-space data are substantially the same. Forevenly distributed data, the difference between a first ky interval anda second ky interval between the odd echoes and/or the even echoescorresponding to the partially filled k-space data may be less than athreshold relating to the ky interval. As used herein, that partiallyfilled k-space data are not evenly distributed may indicate that the kyintervals between the odd echoes and/or the even echoes corresponding tothe partially filled k-space data are substantially not the same. Fornon-evenly distributed data, the difference between a first ky intervaland a second ky interval between the odd echoes and/or the even echoescorresponding to the partially filled k-space data may be no less than athreshold relating to the ky interval.

In some embodiments, a convolution kernel may be determined by datafitting based on a kernel function and one or more data points of thecorresponding data set(s). For the purposes of illustration, anexemplary kernel function may be expressed as Equation (1):S _(l)(k _(x) ,k _(y))=Σ_(l,p,n)(l,k _(x) −pΔk _(x) ,k _(y) −qΔk _(y))S_(l)(l,k _(x) −pΔk _(x) ,k _(y) −qΔk _(y)),  (1)where S_(l)(k_(x), k_(y)) may represent measured data or pre-processeddata of a point (k_(x), k_(y)) of a channel l (or a k-space data set); lmay represent a channel number, (k_(x), k_(y)) may represent a datapoint in k-space; p may represent a location along the readout (k_(x))direction; q may represent a location along the phase encoding (k_(y))direction; and n may represent a weight for the channel l (or a k-spacedata set).

As shown in Equation (1), in the determination of a convolution kernel,the weight n is unknown, and the other parameters are known. Byperforming data fitting, the weight n may be determined. In someembodiments, the data fitting may be performed based on a least squarefitting technique. In some embodiments, one or more weights may bedetermined to form a convolution kernel.

In 903, one or more synthetic data sets may be generated based on theconvolution kernel(s) and the measured data set(s) or the pre-processeddata set(s). The operation 903 may be performed by the synthetic datageneration unit 504. The synthetic data set(s) may be determined ink-space or an intermediate space. A synthetic data set may relate to acorresponding convolution kernel and one or more measured data sets orpre-processed data sets (e.g., all the measured (or pre-processed) datasets). In some embodiments, a synthetic data set may be determined basedon a convolution of a corresponding convolution kernel and the measured(or pre-processed) data sets (e.g., all the measured (or pre-processed)data sets). For example, for a convolution kernel with a 3×3×C (C is thenumber of channels) size (e.g., the convolution kernel 1012 in FIG.10B), a synthetic data set (e.g., the synthetic data set 1022 in FIG.10C) corresponding to the convolution kernel 1012 may be generated bytraversing the data sets (e.g., the measured (or pre-processed) datasets) using the convolution kernel 1012. In some embodiments, one ormore synthetic data sets may be generated, in which each synthetic dataset may be generated based on the measured (or pre-processed) data setsand the corresponding convolution kernel. For example, if there are 9channels (i.e., 9 corresponding measured data sets or pre-processed datasets), the synthetic data generation unit 504 may generate 9 syntheticdata sets.

In some embodiments, if a measured data set or a pre-processed data setincludes a full k-space data set, a corresponding synthetic data set maybe a substantially full k-space data set. In some embodiments, if ameasured data set or a pre-processed data set includes a partiallyfilled k-space data set, a corresponding synthetic data set may still bea partially filled k-space data set. In some embodiments, the syntheticdata generation unit 504 may generate the synthetic data setssimultaneously, or in sequence.

In 905, one or more combined data sets may be generated based on thesynthetic data set(s) and the measured data set(s) or the pre-processeddata set(s). The operation 905 may be performed by the combined datageneration unit 506. The combined data set(s) may be determined ink-space or an intermediate space. A combined data set may relate to acorresponding synthetic data set and a corresponding measured (orpre-processed) data set. In some embodiments, if a synthetic data setincludes a full k-space data set, the corresponding combined data setmay still be a full k-space data set. In some embodiments, if asynthetic data set includes a partially filled k-space data set, thecorresponding combined data set may still be a partially filled k-spacedata set. In some embodiments, a combined data set may be generatedbased on a linear or nonlinear combination of a corresponding syntheticdata set and a corresponding measured (or pre-processed) data set. Insome embodiments, the combination of a corresponding synthetic data setand a corresponding measured (or pre-processed) data set may be realizedbased on a relaxation iteration algorithm, or any other optimizationalgorithm.

Merely by way of example, for each synthetic data set and thecorresponding measured (or pre-processed) data set, the combined datageneration unit 506 may determine one or more weighting factors (orweights). The combined data generation unit 506 may determine a combineddata set based on the weighting factor(s), a corresponding syntheticdata set, and a corresponding measured (or pre-processed) data set. Forexample, the combined data generation unit 506 may determine a weightedsum of the corresponding synthetic data set and the correspondingmeasured (or pre-processed) data set based on the weighting factor(s).In some embodiments, the weighting factor(s) for different k-space datasets may be the same or different. In different iterations, theweighting factor(s) may remain the same or change. In some embodiments,the weighting factor(s) may be changed or adjusted based on thedifference between the combined data sets generated in two or moreconsecutive iterations.

In 907, whether the combined data set(s) satisfy a condition may bedetermined. The operation 907 may be performed by the judgment unit 510.In some embodiments, the condition may relate to the difference betweenthe combined data sets generated in two or more consecutive iterations.The judgment unit 510 may determine whether the difference is greaterthan a first threshold. In response to the determination that thedifference is greater than the first threshold, the judgment unit 510may determine to perform a next iteration, and the process may proceedto 909. In response to the determination that the difference is lowerthan or equal to the first threshold, the judgment unit 510 maydetermine to terminate the iteration(s), and the process may proceed to911. In some embodiments, the condition may relate to an iteration countrepresenting the number of iterations that have been performed. Thejudgment unit 510 may determine whether the iteration count is greaterthan a second threshold. In response to the determination that theiteration count is lower than the second threshold, the judgment unit510 may determine to perform a next iteration, and the process mayproceed to 909. In response to the determination that the iterationcount is greater than or equal to the second threshold, the judgmentunit 510 may determine to terminate the iteration(s), and the processmay proceed to 911. In some embodiments, the first threshold and thesecond threshold may be predetermined according to practical scenarios.The first threshold and/or the second threshold may be part of defaultsettings of the processing device 140, or may be set or adjusted by auser (e.g., a doctor).

In 909, the combined data set(s) may be designated as the measured dataset(s) or the pre-processed data set(s). The operation 909 may beperformed by the data updating unit 508. Before a next iteration isperformed, the data updating unit 508 may designate the combined dataset(s) as the measured (or pre-processed) data set(s). Then the processmay proceed to 901, and a next iteration may be performed. In eachiteration, the measured data set(s) or the pre-processed data set(s),the synthetic data set(s), and/or the combined data set(s) may beupdated. Besides, the points in the convolution kernel(s) may be updatedin different iterations. It should be noted that the convolution kernelsgenerated in different iterations for a same channel may be the same ordifferent. For example, the values of the elements of the convolutionkernels may be different. As another example, the sizes of theconvolution kernels may be the same or different. As a further example,the shapes of the convolution kernels may be the same or different.

In 911, the last generated combined data set(s) may be obtained. In someembodiments, the last generated combined data set(s) may be stored inthe storage device 150 or used in further processing. In someembodiments, the last generated combined data set(s) may be obtained bythe image reconstruction module 440 for reconstructing an image.

It should be noted that the above description of the process forgenerating the combined data set(s) is provided for the purposes ofillustration, and is not intended to limit the scope of the presentdisclosure. For persons having ordinary skills in the art, multiplevariations and modifications may be made under the teachings of thepresent disclosure. However, those variations and modifications do notdepart from the scope of the present disclosure. In some embodiments,the operations 901 through 909 may be performed in k-space. In someembodiments, the operations 901 through 909 may be performed in anintermediate space.

FIGS. 10A-10D are schematic diagrams illustrating exemplary measureddata sets, an exemplary convolution kernel, exemplary synthetic datasets, and exemplary combined data sets according to some embodiments ofthe present disclosure. The measured data sets for multiple channels maybe shown in FIG. 10A. As shown in FIG. 10A, a first measured data set1001 may be obtained from a first channel. A second measured data set1002 may be obtained from a second channel. A third measured data set1003 may be obtained from a third channel. As shown in FIG. 10A, themeasured data sets may have first inconsistencies between multipleechoes. Each measured data set may include a plurality of data points.The first measured data set 1001 may be and/or include a full k-spacedata set or a partially filled k-space data set. The second measureddata set 1002 may be and/or include a full k-space data set or apartially filled k-space data set. The third measured data set 1003 maybe and/or include a full k-space data set or a partially filled k-spacedata set. As shown in FIG. 10A, the data points may misalign in thephase encoding direction, and accordingly, there may be inconsistenciesbetween the even echoes and the odd echoes of the measured data sets.For example, the data point P1, the data point P2, and the data point P3in the first measured data set 1001 in different echoes misalign in thephase encoding direction.

FIG. 10B shows an exemplary convolution kernel 1012 containing multiplechannels. The convolution kernel 1012 may correspond to the measureddata set 1002. The convolution kernel 1012 may be generated based on oneor more measured (or corresponding pre-processed) data sets (e.g., allthe measured (or corresponding pre-processed) data sets) and a kernelfunction (e.g., Equation (1)). For example, a target point (e.g., pointT in the second measured data set 1002) may be fitted using data pointswithin a supporting range (e.g., the supporting range 1005 indicated bya cuboid with a dashed frame in FIG. 10A) of the convolution kernel 1012and a kernel function (e.g., Equation (1)). As shown in FIG. 10B, thesolid points of the convolution kernel 1012 may indicate elementsdetermined by data fitting based on corresponding data points of thefirst measured data set 1001, the second measured data set 1002, and thethird measured data set 1003. In some embodiments, the hollow points ofthe convolution kernel 1012 may indicate there are no elements.

It should be noted that in some embodiments, a portion of the datapoints within the supporting range may be used in data fitting todetermine one or more elements of a convolution kernel. For example, asecond line 1007, a second line 1010, and a second line 1014 may not beused in data fitting to determine the elements (illustrated as the solidpoints in FIG. 10B) of the convolution kernel 1012. As shown in FIG.10A, a first set of data of the first measured data set 1001, a secondset of data of the second measured data set 1002, and a third set ofdata of the third measured data set 1003 may be used in data fitting.The first set of data may include the three data points in the firstline 1006 within the supporting range 1005 and the three data points inthe third line 1008 within the supporting range 1005). The second set ofdata may include the three data points in the first line 1009 within thesupporting range 1005 and the three data points in the third line 1011within the supporting range 1005). The third set of data may include thethree data points in the first line 1013 within the supporting range1005 and the three data points in the third line 1015 within thesupporting range 1005). In some embodiments, the data points in thesecond line 1007 of the first measured data set 1001 within thesupporting range 1005, the data points in the second line 1010 of thesecond measured data set 1002 within the supporting range 1005, and thedata points in the second line 1014 of the second measured data set 1003within the supporting range 1005 may not be used in data fitting. Insome embodiments, if the data points in the second line 1007 of thefirst measured data set 1001 within the supporting range 1005, the datapoints in the second line 1010 of the second measured data set 1002within the supporting range 1005, and the data points in the second line1014 of the second measured data set 1003 within the supporting range1005 are used in data fitting, then corresponding elements may be addedin the convolution kernel 1012 at the hollow points, and thus, thehollow points may be converted to solid points.

Similarly, one or more target points in a measured (or correspondingpre-processed) data set (e.g., the measured data set 1002) may be fittedusing data points within the supporting range by traversing the measured(or corresponding pre-processed) data sets (e.g., all the measured (orcorresponding pre-processed) data sets). The data fitting may beperformed based on a least square fitting technique, and one or moreweights may be determined. Thus, the convolution kernel 1012 may bedetermined based on the weights generated by the data fitting.Similarly, a first convolution kernel (not shown in FIG. 10B)corresponding to the measured data set 1001 (or the correspondingpre-processed data set) and/or a third convolution kernel (not shown inFIG. 10B) corresponding to the measured data set 1003 (or thecorresponding pre-processed data set) may be determined.

The convolution kernel 1012 shown in FIG. 10B having a 2×3 (the channeldimension is omitted) size or 3×3×3 (or 3×3 for simplicity) is merely anexample, and the convolution kernel 1012 may have other sizes and/orshapes. For example, the convolution kernel may have a 3×4×3 (or 3×4 forsimplicity) size, 4×2×3 (or 4×2 for simplicity) size, etc. In someembodiments, convolution kernels for different channels may havedifferent sizes. For example, a first convolution kernel may have a3×3×3 (or 3×3 for simplicity) size, a second convolution kernel may havea 5×7×3 (or 5×7 for simplicity) size, and a third convolution kernel mayhave a 7×3×3 (or 7×3 for simplicity) size.

As shown in FIG. 10C, a second synthetic data set 1022 may be generatedbased on a convolution of the measured (or pre-processed) data sets(e.g., the first measured data set 1001, the second measured data set1002, and the third measured data set 1003) and the convolution kernel1012. In each convolution, a data point of the second synthetic data set1022 (e.g., point B shown in FIG. 10C) corresponding to the center ofthe convolution kernel 1012 (e.g., point A shown in FIG. 10B) may bedetermined based on a weighted sum of all the elements of theconvolution kernel 1012 (e.g., the data points illustrated as solid dotsin FIG. 10B) and the corresponding elements of the first measured dataset 1001, the second measured data set 1002, and the third measured dataset 1003 (e.g., the elements within the supporting range 1005 excludingthe second line 1007, the second line 1010, and the second line 1014).All the data points of the second synthetic data set 1022 may bedetermined by traversing the convolution kernel 1012 in the firstmeasured data set 1001, the second measured data set 1002, and the thirdmeasured data set 1003. As the convolution kernel 1012 traverses themeasured (or pre-processed) data sets, the synthetic data set 1022 maybe determined by summing up all the data points in the supporting rangeusing weights provided by the convolution kernel 1012. Similarly, thefirst synthetic data set 1021 and the third synthetic data set 1023 maybe determined based on a convolution of the measured (or pre-processed)data sets (e.g., the first measured data set 1001, the second measureddata set 1002, and the third measured data set 1003) and thecorresponding convolution kernel (e.g., the first convolution kernel andthe third convolution kernel not shown in FIG. 10B). As shown in FIG.10C, the synthetic data set(s) may have second inconsistencies betweenmultiple echoes. The second inconsistencies may be different from thefirst inconsistencies.

As shown in FIG. 10D, a first combined data set 1031 may be generatedbased on a combination of the first measured data set 1001 (orcorresponding pre-processed data set) and the first synthetic data set1021. A second combined data set 1032 may be generated based on acombination of the second measured data set 1002 (or correspondingpre-processed data set) and the second synthetic data set 1022. A thirdcombined data set 1033 may be generated based on a combination of thethird measured data set 1003 (or corresponding pre-processed data set)and the third synthetic data set 1023. As shown in FIG. 10D, theinconsistencies in the combined data set(s) may be substantiallyeliminated in the combined data sets obtained by combining the measureddata set(s) and the synthetic data set(s). It should be noted that themeasured data set(s) (or the synthetic data set(s), or the combined dataset(s)) are merely examples, and are not intended to limit the scope ofthe present disclosure. For example, the number of data sets (orchannels) may be any integer larger than 1. As another example, theodd-even line inconsistencies may have other forms, e.g., overall phasedifferences and shifts along the phase encoding direction and/or thereadout direction, etc. As still another example, the measured data setsshown in FIG. 10A may be replaced with pre-processed data sets, and thecombined data sets may be similarly generated.

FIGS. 11A and 11B are exemplary images processed by 1D correction withdifferent brightness. Before reconstructing the images, the measureddata set(s) were corrected by performing a one-dimensional correctionaccording to process 800 of FIG. 8. The image in FIG. 11B has a higherbrightness than FIG. 11A. As shown in FIG. 11B, Nyquist ghost artifactcan be seen in the image.

FIGS. 11C and 11D are exemplary images processed by 2D correction withdifferent brightness. Before image reconstruction, the measured dataset(s) were corrected by performing a 1D correction according to process800 of FIG. 8 and a 2D correction according to process 900 of FIG. 9.The image in FIG. 11D has higher brightness than FIG. 11C. As shown inFIG. 11D, the image includes reduced Nyquist ghost artifact or noNyquist ghost artifact is clearly visible.

Having thus described the basic concepts, it may be rather apparent tothose skilled in the art after reading this detailed disclosure that theforegoing detailed disclosure is intended to be presented by way ofexample only and is not limiting. Various alterations, improvements, andmodifications may occur and are intended to those skilled in the art,though not expressly stated herein. These alterations, improvements, andmodifications are intended to be suggested by this disclosure, and arewithin the spirit and scope of the exemplary embodiments of thisdisclosure.

Moreover, certain terminology has been used to describe embodiments ofthe present disclosure. For example, the terms “one embodiment,” “anembodiment,” and/or “some embodiments” mean that a particular feature,structure or characteristic described in connection with the embodimentis included in at least one embodiment of the present disclosure.Therefore, it is emphasized and should be appreciated that two or morereferences to “an embodiment” or “one embodiment” or “an alternativeembodiment” in various portions of this specification are notnecessarily all referring to the same embodiment. Furthermore, theparticular features, structures or characteristics may be combined assuitable in one or more embodiments of the present disclosure.

Further, it will be appreciated by one skilled in the art, aspects ofthe present disclosure may be illustrated and described herein in any ofa number of patentable classes or context including any new and usefulprocess, machine, manufacture, or composition of matter, or any new anduseful improvement thereof. Accordingly, aspects of the presentdisclosure may be implemented entirely hardware, entirely software(including firmware, resident software, micro-code, etc.) or combiningsoftware and hardware implementation that may all generally be referredto herein as a “unit,” “module,” or “system.” Furthermore, aspects ofthe present disclosure may take the form of a computer program productembodied in one or more computer readable media having computer readableprogram code embodied thereon.

A non-transitory computer readable signal medium may include apropagated data signal with computer readable program code embodiedtherein, for example, in baseband or as part of a carrier wave. Such apropagated signal may take any of a variety of forms, includingelectro-magnetic, optical, or the like, or any suitable combinationthereof. A computer readable signal medium may be any computer readablemedium that is not a computer readable storage medium and that maycommunicate, propagate, or transport a program for use by or inconnection with an instruction execution system, apparatus, or device.Program code embodied on a computer readable signal medium may betransmitted using any appropriate medium, including wireless, wireline,optical fiber cable, RF, or the like, or any suitable combination of theforegoing.

Computer program code for carrying out operations for aspects of thepresent disclosure may be written in any combination of one or moreprogramming languages, including an object oriented programming languagesuch as Java, Scala, Smalltalk, Eiffel, JADE, Emerald, C++, C#, VB. NET,Python or the like, conventional procedural programming languages, suchas the “C” programming language, Visual Basic, Fortran 2003, Perl, COBOL2002, PHP, ABAP, dynamic programming languages such as Python, Ruby andGroovy, or other programming languages. The program code may executeentirely on the user's computer, partly on the user's computer, as astand-alone software package, partly on the user's computer and partlyon a remote computer or entirely on the remote computer or server. Inthe latter scenario, the remote computer may be connected to the user'scomputer through any type of network, including a local area network(LAN) or a wide area network (WAN), or the connection may be made to anexternal computer (for example, through the Internet using an InternetService Provider) or in a cloud computing environment or offered as aservice such as a Software as a Service (SaaS).

Furthermore, the recited order of processing elements or sequences, orthe use of numbers, letters, or other designations therefore, is notintended to limit the claimed processes and methods to any order exceptas may be specified in the claims. Although the above disclosurediscusses through various examples what is currently considered to be avariety of useful embodiments of the disclosure, it is to be understoodthat such detail is solely for that purpose, and that the appendedclaims are not limited to the disclosed embodiments, but, on thecontrary, are intended to cover modifications and equivalentarrangements that are within the spirit and scope of the disclosedembodiments. For example, although the implementation of variouscomponents described above may be embodied in a hardware device, it mayalso be implemented as a software only solution, e.g., an installationon an existing server or mobile device.

Similarly, it should be appreciated that in the foregoing description ofembodiments of the present disclosure, various features are sometimesgrouped together in a single embodiment, figure, or description thereoffor the purpose of streamlining the disclosure aiding in theunderstanding of one or more of the various inventive embodiments. Thismethod of disclosure, however, is not to be interpreted as reflecting anintention that the claimed subject matter requires more features thanare expressly recited in each claim. Rather, inventive embodiments liein less than all features of a single foregoing disclosed embodiment.

In some embodiments, the numbers expressing quantities, properties, andso forth, used to describe and claim certain embodiments of theapplication are to be understood as being modified in some instances bythe term “about,” “approximate,” or “substantially.” For example,“about,” “approximate,” or “substantially” may indicate ±20% variationof the value it describes, unless otherwise stated. Accordingly, in someembodiments, the numerical parameters set forth in the writtendescription and attached claims are approximations that may varydepending upon the desired properties sought to be obtained by aparticular embodiment. In some embodiments, the numerical parametersshould be construed in light of the number of reported significantdigits and by applying ordinary rounding techniques. Notwithstandingthat the numerical ranges and parameters setting forth the broad scopeof some embodiments of the application are approximations, the numericalvalues set forth in the specific examples are reported as precisely aspracticable.

Each of the patents, patent applications, publications of patentapplications, and other material, such as articles, books,specifications, publications, documents, things, and/or the like,referenced herein is hereby incorporated herein by this reference in itsentirety for all purposes, excepting any prosecution file historyassociated with same, any of same that is inconsistent with or inconflict with the present document, or any of same that may have alimiting affect as to the broadest scope of the claims now or laterassociated with the present document. By way of example, should there beany inconsistency or conflict between the description, definition,and/or the use of a term associated with any of the incorporatedmaterial and that associated with the present document, the description,definition, and/or the use of the term in the present document shallprevail.

In closing, it is to be understood that the embodiments of theapplication disclosed herein are illustrative of the principles of theembodiments of the application. Other modifications that may be employedmay be within the scope of the application. Thus, by way of example, butnot of limitation, alternative configurations of the embodiments of theapplication may be utilized in accordance with the teachings herein.Accordingly, embodiments of the present application are not limited tothat precisely as shown and described.

What is claimed is:
 1. A method implemented on a computing device havingat least one processor, at least one computer-readable storage medium,and a communication port connected to an imaging device, the imagingdevice including a plurality of radiofrequency (RF) coils for receivinga plurality of channels of magnetic resonance (MR) signals, the methodcomprising: a) obtaining a plurality of measured data sets generated byscanning a subject using the imaging device, each measured data setcorresponding to a channel of MR signal received by an RF coil; b)determining, based on the plurality of measured data sets, in a dataspace, a plurality of convolution kernels, each convolution kernelrelating to all of the plurality of measured data sets, each convolutionkernel corresponding to a channel of MR signal received by an RF coil;c) generating, based on the plurality of convolution kernels and theplurality of measured data sets, in the data space, a plurality ofsynthetic data sets, wherein each synthetic data set is generated basedon one or more of the plurality of measured data sets and acorresponding convolution kernel of the plurality of convolutionkernels, and wherein each synthetic data set and the correspondingconvolution kernel correspond to a same channel; d) generating, based onthe plurality of synthetic data sets and the plurality of measured datasets, in the data space, a plurality of combined data sets, eachcombined data set relating to one of the plurality of synthetic datasets and a corresponding measured data set of the plurality of measureddata sets; and e) reconstructing, based on the plurality of combineddata sets, an image using an inverse Fourier transform.
 2. The method ofclaim 1, wherein the plurality of measured data sets are generated byecho planar imaging (EPI) using the imaging device.
 3. The method ofclaim 1, wherein the plurality of measured data sets are pre-processedby performing a preliminary correction for the plurality of measureddata sets.
 4. The method of claim 1, further comprising: performing aplurality of iterations, and in each current iteration, designating theplurality of combined data sets generated in a previous iteration as theplurality of measured data sets; repeating b)-d) to update the pluralityof combined data sets; and determining whether the plurality of updatedcombined data sets generated in the current iteration satisfy atermination criterion.
 5. The method of claim 4, wherein the terminationcriterion relates to a difference between the plurality of combined datasets generated in the previous iteration and the plurality of updatedcombined data sets generated in the current iteration.
 6. The method ofclaim 4, wherein at least two convolution kernels for a same channelgenerated in different iterations are different.
 7. The method of claim1, wherein each measured data set of the plurality of measured data setsincludes a full k-space data set.
 8. The method of claim 7, wherein thereconstructing an image comprises: processing the plurality of combineddata sets with an inverse Fourier transform to generate the image. 9.The method of claim 1, wherein at least one measured data set of theplurality of measured data sets includes a partially filled k-space dataset.
 10. The method of claim 9, wherein the reconstructing an imagecomprises: for each measured data set including a partially filledk-space data set, filling, based on at least a portion of the pluralityof combined data sets, a corresponding combined data set to reconstructa full k-space data set; and processing a plurality of full k-space datasets corresponding to the plurality of combined data sets with aninverse Fourier transform to generate the image.
 11. The method of claim1, wherein the data space is k-space.
 12. The method of claim 1, whereinthe data space is an intermediate space between k-space and an imagespace, the method further comprising: determining the intermediate spaceby processing k-space with a one-dimensional (1D) inverse Fouriertransform.
 13. The method of claim 1, wherein at east two convolutionkernels of the plurality of convolution kernels are different.
 14. Themethod of claim 1, wherein the generating a plurality of combined datasets comprises; determining, based on a plurality of weighting factors,a weighted sum of the plurality of synthetic data sets and the pluralityof measured data sets to obtain the plurality of combined data sets,wherein each combined data set is determined based on a portion of theplurality of weighting factors, one of the plurality of synthetic datasets, and a corresponding measured data set of the plurality of measureddata sets.
 15. A magnetic resonance imaging (MRI) method, comprising:generating a plurality of magnetic resonance (MR) signals by scanning asubject using an imaging device; receiving the plurality of MR signalsusing a plurality of radiofrequency (RF) coils of the imaging device;obtaining a plurality of measured k-space data sets by entering the MRsignals into k-space, each measured k-space data set corresponding toone of the plurality of RF coils; performing one or more corrections forthe plurality of measured k-space data sets to obtain a plurality ofcorrected k-space data sets; and reconstructing, based on the pluralityof corrected k-space data sets, an image related to the subject using aninverse Fourier transform, wherein the one or more corrections comprise:determining, based on the plurality of measured k-space data sets, aplurality of convolution kernels; generating, based on the plurality ofconvolution kernels and the plurality of measured k-space data sets, aplurality of synthetic k-space data sets; and generating, based on theplurality of synthetic k-space data sets and the plurality of measuredk-space data sets, the plurality of corrected k-space data sets.
 16. Themethod of claim 15, further comprising: before determining the pluralityof convolution kernels, performing a linear or non-linear correction forthe plurality of measured k-space data sets.
 17. The method of claim 15,wherein the determining a plurality of convolution kernels comprises:processing the plurality of measured k-space data sets withone-dimensional (1D) inverse Fourier transform to obtain an intermediateimage; and determining, based on the intermediate image, the pluralityof convolution kernels.
 18. A system, comprising: at least one storagemedium storing a set of instructions; at least one processor incommunication with the at least one storage medium; and a communicationport connected to an imaging device, the imaging device including aplurality of radiofrequency (RF) coils for receiving a plurality ofchannels of magnetic resonance (MR) signals; wherein when executing theset of instructions, the at least one processor is configured to causethe system to: a) obtain a plurality of measured data sets generated byscanning a subject using the imaging device, each measured data setcorresponding to a channel of MR signal received by an RF coil; b)determine, based on the plurality of measured data sets, in a dataspace, a plurality of convolution kernels, each convolution kernelrelating to all of the plurality of measured data sets, each convolutionkernel corresponding to a channel of MR signal received by an RF coil;c) generate, based on the plurality of convolution kernels and theplurality of measured data sets, in the data space, a plurality ofsynthetic data sets, wherein each synthetic data set is generated basedon one or more of the plurality of measured data sets and a convolutionkernel of the plurality of convolution kernels, and wherein eachsynthetic data set and the convolution kernel correspond to a samechannel; d) generate, based on the plurality of synthetic data sets andthe plurality of measured data sets, in the data space, a plurality ofcombined data sets, each combined data set relating to one of theplurality of synthetic data sets and a corresponding measured data setof the plurality of measured data sets; and e) reconstruct, based on theplurality of combined data sets, an image using an inverse Fouriertransform.
 19. The system of claim 18, wherein at least one measureddata set of the plurality of measured data sets includes a partiallyfilled k-space data set.
 20. The system of claim 18, wherein the dataspace is k-space or an intermediate space between k-space and an imagespace.